Several companies provide such services; they allow you to put code on your site such that users can sign up for e-mail addresses based on your domain. Even Google offers a service like this, which would give users an interface similar to the Gmail interface:
Gmail for Your Domain
If you don't want to subject users to advertising, or would like to retain control of the service (avoid having to change e-mail settings, etc.), other companies sell software for installation on your server. For example,
Alt-N Technologies sells software, based on the number of users, that looks like an online version of Outlook (called LookOut).
There are many other such services available, that offer a variety of appealing domains themed around hobbies, careers, interests, etc.
I am curious, do you anticipate a lot of demand from people who find a dikkop e-mail address appealing?
-- Duncan