I have a User model, which has an email and a password field. For security, these may not be equal to each other. How can I define this in my model?
Create custom validataion:
validate :check_email_and_password
def check_email_and_password
  errors.add(:password, "can't be the same as email") if email == password
end
But keep in mind that storing password as a plain text is bad idea. You should store it hashed. Try some authentication plugin like authlogic or Restful authentication.
It depends how Your password is stored:
class User < ActiveRecord::Base
    validate :email_and_password_validation
    def email_and_password_validation
        if self.email == self.password
            errors.add_to_base("Password must be different from email") 
        end
    end
end
This would work if Your password is stored literally, but You can perform the same thing with email (e.g. create a hashed version) and check for equality with password. E.g:
class User < ActiveRecord::Base
    validate :email_and_password_validation
    def email_and_password_validation
        if make_hash(self.email) == self.hashed_password
            errors.add_to_base("Password must be different from email") 
        end
    end
end
My example is taken from http://api.rubyonrails.org/classes/ActiveRecord/Validations/ClassMethods.html#M002162
Your situation is quite general so You can be interested in creating custom validation method. Everything is covered here: http://guides.rubyonrails.org/active_record_validations_callbacks.html#creating-custom-validation-methods
more fun:
  validates :password, exclusion: { in: ->(person) { [person.email] }, message: "cannot use protected password" }
which might be even better in this case, since you could check for other forbidden values with something like
  validates :password, exclusion: { in: ->(person) { [person.email, person.first_name, person.last_name, person.phone_number, person.department_name] }, message: "cannot use protected password" }
                                                                        all you need is to create validation rule in your model for example
class User < ActiveRecord::Base
  def validate_on_create
    if email == password
      errors.add("password", "email and password can't be the same")
    end
  end
end
                                                                        You can use a custom validation method to check this.
class User < ActiveRecord::Base
  # ...
  def validate
    if (self.email == self.password)
      errors.add(:password, "password cannot equal email")
      errors.add(:email, "email cannot equal password")
    end
  end
end
                                                                        If you want to support multiple languages, you have to come up with another solution, which translates the error messages and the attribute names. So I created a new each validator for that.
validators/values_not_equal_validator.rb:
class ValuesNotEqualValidator < ActiveModel::EachValidator
  def validate(record)
    @past = Hash.new
    super
  end
  def validate_each(record, attribute, value)
    @past.each do |k, v|
      if v == value
        record.errors.add(attribute, I18n.t('errors.messages.should_not_be_equal_to') + " " + record.class.human_attribute_name(k))
      end
    end
    @past[attribute] = value
  end
end
I call it in the model like this:
class User < ActiveRecord::Base
  validates :forename, :surname, values_not_equal: true
end
And I translate it the messages like this:
de:
  activerecord:
    attributes:
      user:
        forename: 'Vorname'
        surname: 'Nachname'
  errors:
    messages:
      should_not_be_equal_to: 'darf nicht gleich sein wie'