If you have your DNS hosted in one place (say DNS Made Easy) but host your content on 1and1.com. 1and1 allows you to do this without transferring the domain to them. The problem is they appear to not set the DirectoryIndex directive for hosts using external DNS. This can be overcome with either creating or adding to the .htaccess file in your site’s root directory:
That’ll work for WordPress, or most other PHP-based sites. You can always change it to index.html if that’s what your site’s index page is.