Close Window from ViewModel

I usually put an event on the view model when I need to do this and then hook it up to the Window.Close() when binding the view model to the window

public class LoginViewModel
{
    public event EventHandler OnRequestClose;

    private void Login()
    {
        // Login logic here
        OnRequestClose(this, new EventArgs());
    }
}

And when creating the login window

var vm = new LoginViewModel();
var loginWindow = new LoginWindow
{
    DataContext = vm
};
vm.OnRequestClose += (s, e) => loginWindow.Close();

loginWindow.ShowDialog(); 

You can pass the window to your ViewModel using the CommandParameter. See my Example below.

I've implemented an CloseWindow Method which takes a Windows as parameter and closes it. The window is passed to the ViewModel via CommandParameter. Note that you need to define an x:Name for the window which should be close. In my XAML Window i call this method via Command and pass the window itself as a parameter to the ViewModel using CommandParameter.

Command="{Binding CloseWindowCommand, Mode=OneWay}" 
CommandParameter="{Binding ElementName=TestWindow}"

ViewModel

public RelayCommand<Window> CloseWindowCommand { get; private set; }

public MainViewModel()
{
    this.CloseWindowCommand = new RelayCommand<Window>(this.CloseWindow);
}

private void CloseWindow(Window window)
{
    if (window != null)
    {
       window.Close();
    }
}

View

<Window x:Class="ClientLibTestTool.ErrorView"
        x:Name="TestWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:localization="clr-namespace:ClientLibTestTool.ViewLanguages"
        DataContext="{Binding Main, Source={StaticResource Locator}}"
        Title="{x:Static localization:localization.HeaderErrorView}"
        Height="600" Width="800"
        ResizeMode="NoResize"
        WindowStartupLocation="CenterScreen">
    <Grid> 
        <Button Content="{x:Static localization:localization.ButtonClose}" 
                Height="30" 
                Width="100" 
                Margin="0,0,10,10" 
                IsCancel="True" 
                VerticalAlignment="Bottom" 
                HorizontalAlignment="Right" 
                Command="{Binding CloseWindowCommand, Mode=OneWay}" 
                CommandParameter="{Binding ElementName=TestWindow}"/>
    </Grid>
</Window>

Note that i'm using the MVVM light framework, but the principal applies to every wpf application.

This solution violates of the MVVM pattern, because the view-model shouldn't know anything about the UI Implementation. If you want to strictly follow the MVVM programming paradigm you have to abstract the type of the view with an interface.

MVVM conform solution (Former EDIT2)

the user Crono mentions a valid point in the comment section:

Passing the Window object to the view model breaks the MVVM pattern IMHO, because it forces your vm to know what it's being viewed in.

You can fix this by introducing an interface containing a close method.

Interface:

public interface ICloseable
{
    void Close();
}

Your refactored ViewModel will look like this:

ViewModel

public RelayCommand<ICloseable> CloseWindowCommand { get; private set; }

public MainViewModel()
{
    this.CloseWindowCommand = new RelayCommand<IClosable>(this.CloseWindow);
}

private void CloseWindow(ICloseable window)
{
    if (window != null)
    {
        window.Close();
    }
}

You have to reference and implement the ICloseable interface in your view

View (Code behind)

public partial class MainWindow : Window, ICloseable
{
    public MainWindow()
    {
        InitializeComponent();
    }
}

Answer to the original question: (former EDIT1)

Your Login Button (Added CommandParameter):

<Button Name="btnLogin" IsDefault="True" Content="Login" Command="{Binding ShowLoginCommand}" CommandParameter="{Binding ElementName=LoginWindow}"/>

Your code:

 public RelayCommand<Window> CloseWindowCommand { get; private set; } // the <Window> is important for your solution!

 public MainViewModel() 
 {
     //initialize the CloseWindowCommand. Again, mind the <Window>
     //you don't have to do this in your constructor but it is good practice, thought
     this.CloseWindowCommand = new RelayCommand<Window>(this.CloseWindow);
 }

 public bool CheckLogin(Window loginWindow) //Added loginWindow Parameter
 {
    var user = context.Users.Where(i => i.Username == this.Username).SingleOrDefault();

    if (user == null)
    {
        MessageBox.Show("Unable to Login, incorrect credentials.");
        return false;
    }
    else if (this.Username == user.Username || this.Password.ToString() == user.Password)
    {
        MessageBox.Show("Welcome "+ user.Username + ", you have successfully logged in.");
        this.CloseWindow(loginWindow); //Added call to CloseWindow Method
        return true;
    }
    else
    {
        MessageBox.Show("Unable to Login, incorrect credentials.");
        return false;
    }
 }

 //Added CloseWindow Method
 private void CloseWindow(Window window)
 {
     if (window != null)
     {
         window.Close();
     }
 }