As Tim Berners-Lee told at TED, there's lots of hidden data. What useful free databases or APIs you know around web? For example:
There's a lot of resources listed in this article (and the comments too) at Read Write Web: Where to find open data on the web
See also the ProgrammableWeb API Dashboard — APIs are listed by category and popularity.
The IP address Geotargeting API is a good one, it isn't really a database but its handy to make lookups.
The Zip Code Database Project - A database containing the fully city/state as well as coordinates for every zip code in the US. I've used it in numerous projects for handy city/state zip code lookups.
reCAPTCHA... provides offsite CAPTCHA generation and validation.
The UC Irvine Machine Learning Repository - for data mining research