How to update only one field using Entity Framework?

You can tell EF which properties have to be updated in this way:

public void ChangePassword(int userId, string password)
{
  var user = new User { Id = userId, Password = password };
  using (var context = new ObjectContext(ConnectionString))
  {
    var users = context.CreateObjectSet<User>();
    users.Attach(user);
    context.ObjectStateManager.GetObjectStateEntry(user)
      .SetModifiedProperty("Password");
    context.SaveChanges();
  }
}

Ladislav's answer updated to use DbContext (introduced in EF 4.1):

public void ChangePassword(int userId, string password)
{
    var user = new User() { Id = userId, Password = password };
    using (var db = new MyEfContextName())
    {
        db.Users.Attach(user);
        db.Entry(user).Property(x => x.Password).IsModified = true;
        db.SaveChanges();
    }
}