How to localize ASP.NET Identity UserName and Password error messages?

ASP NET Core workaround (25.11.2016)

You can inject IStringLocalizer into custom IdentityErrorDescriber

1) Create custom IdentityErrorDescriber (see Gerardo Grignoli answer)

public class MultilanguageIdentityErrorDescriber : IdentityErrorDescriber
{
    private readonly IStringLocalizer<SharedResource> _localizer;

    public MultilanguageIdentityErrorDescriber(IStringLocalizer<SharedResource> localizer)
    {
        _localizer = localizer;
    }

    public override IdentityError DuplicateEmail(string email)
    {
        return new IdentityError()
        {
            Code = nameof(DuplicateEmail),
            Description = string.Format(_localizer["Email {0} is already taken."], email)
        };
    }

    // DuplicateUserName, InvalidEmail, DuplicateUserName etc
}

2) Register MultilanguageIdentityErrorDescriber in Startup.cs

services.AddIdentity<IdentityUser, IdentityRole>()
            .AddErrorDescriber<MultilanguageIdentityErrorDescriber>()
            .AddDefaultTokenProviders();

3) Add error messages to SharedResource.language.resx.

As of version 2 of identity which released on 20 march 2014 you can now have localized error messages.

First install the identity localized package.

Install-Package Microsoft.AspNet.Identity.Core.fr

Then the proper culture must be set in order to get localized messages for example one way to set culture is in web.config

<system.web>
      <globalization culture="fr-FR" uiCulture="fr"/>
</system.web>

For ASP.NET Core: (Microsoft.AspNetCore.Identity 1.0.0)

Create a class that inherits IdentityErrorDescriber and override the desired error messages.

public class CustomIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"An unknown failure has occurred." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Optimistic concurrency failure, object has been modified." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Incorrect password." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Invalid token." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "A user with this login already exists." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"User name '{userName}' is invalid, can only contain letters or digits." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"Email '{email}' is invalid."  }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"User Name '{userName}' is already taken."  }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"Email '{email}' is already taken."  }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"Role name '{role}' is invalid."  }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"Role name '{role}' is already taken."  }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "User already has a password set." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "Lockout is not enabled for this user." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"User already in role '{role}'."  }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"User is not in role '{role}'."  }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"Passwords must be at least {length} characters."  }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "Passwords must have at least one non alphanumeric character." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "Passwords must have at least one digit ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "Passwords must have at least one lowercase ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "Passwords must have at least one uppercase ('A'-'Z')." }; }
}

On your Startup class, register the custom ErrorDescriber inside ConfigureServices:

services.AddIdentity<ApplicationUser, IdentityRole>()
                .AddErrorDescriber<CustomIdentityErrorDescriber>(); // Add this line

UPDATE: Below you can find already translated versions for spanish and portuguese. Double check them!

public class SpanishIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"Ha ocurrido un error." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Ha ocurrido un error, el objeto ya ha sido modificado (Optimistic concurrency failure)." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Password Incorrecta." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Ha ingresado un código Inválido." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "Un usuario con ese nombre ya existe." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"El nombre de usuario '{userName}' es inválido. Solo puede contener letras y números." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"La dirección de email '{email}' es incorrecta."  }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"El usuario '{userName}' ya existe, por favor ingrese un nombre diferente."  }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"La direccion de email '{email}' ya se encuentra registrada. Puede recupar su contraseña para ingresar nuevamente al sistema."  }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"El nombre de rol '{role}' es inválido."  }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"El nombre de rol '{role}' ya existe."  }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "El usuario ya tiene contraseña." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "El bloqueo no esta habilitado para este usuario." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"El usuario ya es parte del rol '{role}'."  }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"El usuario no es parte del rol '{role}'."  }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"La contraseña deben tener un largo mínimo de {length} caracteres."  }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "La contraseña debe contener al menos un caracter alfanumérico." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "La contraseña debe incluir al menos un dígito ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "La contraseña debe incluir al menos una letra minúscula ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "La contraseña debe incluir al menos una letra MAYÚSCULA ('A'-'Z')." }; }
}

Portuguese: (many thanks to furlanrapha)

public class PortugueseIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"Um erro desconhecido ocorreu." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Falha de concorrência otimista, o objeto foi modificado." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Senha incorreta." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Token inválido." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "Já existe um usuário com este login." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"Login '{userName}' é inválido, pode conter apenas letras ou dígitos." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"Email '{email}' é inválido." }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"Login '{userName}' já está sendo utilizado." }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"Email '{email}' já está sendo utilizado." }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"A permissão '{role}' é inválida." }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"A permissão '{role}' já está sendo utilizada." }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "Usuário já possui uma senha definida." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "Lockout não está habilitado para este usuário." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"Usuário já possui a permissão '{role}'." }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"Usuário não tem a permissão '{role}'." }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"Senhas devem conter ao menos {length} caracteres." }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "Senhas devem conter ao menos um caracter não alfanumérico." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "Senhas devem conter ao menos um digito ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "Senhas devem conter ao menos um caracter em caixa baixa ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "Senhas devem conter ao menos um caracter em caixa alta ('A'-'Z')." }; }
}

this is for dear Farsi(Persian) speakers

using Microsoft.AspNetCore.Identity;

namespace WebApplication.Admin.Helpers
{
    public class CustomIdentityErrorDescriber : IdentityErrorDescriber
    {
        public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"یک خطای ناشناخته رخ داده است." }; }
        public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "رکورد جاری پیشتر ویرایش شده‌است و تغییرات شما آن‌را بازنویسی خواهد کرد." }; }
        public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "کلمه عبور نادرست است." }; }
        public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "کلمه عبور نامعتبر است." }; }
        public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "این کاربر قبلأ اضافه شده‌است." }; }
        public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"نام کاربری '{userName}' نامعتبر است، فقط می تواند حاوی حروف ویا اعداد باشد." }; }
        public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"ایمیل '{email}' نامعتبر است." }; }
        public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"این نام کاربری '{userName}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"ایمیل '{email}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"نام نقش '{role}' نامعتبر است." }; }
        public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"این نام نقش '{role}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "کلمه‌ی عبور کاربر قبلأ تنظیم شده‌است." }; }
        public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "این کاربر فعال است." }; }
        public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"این نقش '{role}' قبلأ به این کاربر اختصاص یافته است." }; }
        public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"این نقش '{role}' قبلأ به این کاربر اختصاص نیافته است." }; }
        public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"کلمه عبور باید حداقل {length} کاراکتر باشد." }; }
        public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "کلمه عبور باید حداقل یک کاراکتر غیر از حروف الفبا داشته باشد." }; }
        public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "کلمه عبور باید حداقل یک عدد داشته باشد." }; }
        public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "کلمه عبور باید حداقل یک حرف کوچک داشته باشد." }; }
        public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "کلمه عبور باید حداقل یک حرف بزرگ داشته باشد." }; }
        public override IdentityError RecoveryCodeRedemptionFailed() { return new IdentityError { Code = nameof(RecoveryCodeRedemptionFailed), Description = "بازیابی ناموفق بود." }; }
        public override IdentityError PasswordRequiresUniqueChars(int uniqueChars) { return new IdentityError { Code = nameof(PasswordRequiresUniqueChars), Description = $"کلمه عبور باید حداقل داراى {uniqueChars} حرف متفاوت باشد." }; }
    }
}