One of the most effective ways to find a free domain name that is relevant to your site is to grab a keyword and add prefixes or suffixes to it, until you find something unique. Suppose you want to launch a blog about marketing, all you have to do is pick the word marketing and start adding prefixes like “emarketing.com”, “promarketing.com”, “polimarketing.com” or suffixes like “marketingspot.com”, “marketingvox.com” or “marketingpulse.com”.
I look forward to reading about your winners in the comments. Now if you'll excuse me, I'm off to register hyperLindsayLohandata.info and make millions.
Update: Now the script lets you choose whether you want prefix, suffix, or both. Thanks Daniel!
Another update: Corrected the links to my other site, which has changed hosts.