Perplexus, formerly a subsite of Floogle.com, offers a variety of user-submitted and -graded puzzles: logic, math, paradoxes, and riddles, to name a few. There is a strict limit of two new puzzles added daily, which means only the best submissions are posted; as a result, the quality of the writing is generally better than that found on other user-run sites.
It is easy to find the most recent problems, since they are posted first on the main page. One nice feature is that when the puzzles are first posted, the official answers aren't for a couple days - so there's no temptation to cheat and just look at the answer. In fact, for the adventurous, they maintain a directory just for puzzles that haven't been solved yet.
If you're in the mood to solve any puzzle they can throw at you, just click a button and be presented with a random problem from their archives. You can also link to a random daily puzzle from your own website, like we've done here.
