Obama Math Challenge – includes problems allegedly pulled from Singapore’s math curriculum, many of which are useful archetypes for ways to get kids to think.
Art of Problem Solving (wiki) – I need to check this out, and I forget why I opened it in my browser. But just the idea of a wiki with this title makes me think that it’s a good idea to include it here.
Martin Gardener Puzzles
Car Talk Puzzlers
LSAT Analytical Reasoning Questions
The following web sites may be useful:
http://www.cut-the-knot.org/ – excellent source of interesting problems and their solutions
http://mathforum.org – the Ask Dr. Math section has a lot of interesting questions (like why do two negatives multiply together to equal a positive
Challenging, but a good place to find ideas: