Since you should aim to have no more than four DNS lookups per page, it may be tricky to integrate third-party content such as Flickr images or ads that are hosted on a third-party server. Also, hotlinking images (by placing on your page an <img /> tag whose src attribute points to a file on another person's server) not only steals bandwidth from the other site, but also harms your own page's performance, causing an extra DNS lookup.
If your site contains user-generated content (as do forums, for example), you can't easily prevent multiple DNS lookups, since users could potentially post images located anywhere on the Web. You could write a script that copies each image from a user's post to your server, but that approach can get fairly complicated.
Aim for the low-hanging fruit. For example, in the phpBB forum software, you can configure whether users need to hotlink their avatar images or upload them to your server. In this case, uploaded avatars will result in better performance for your site.