Here are some really good puzzles I've come across over the years in books, online and from just talking with people. Most of them don't require much math (the first two are really simple), but all require some degree of logic, common sense, and inuition. Some are pretty difficult and might take a long time and complex logic to figure out (but are nevertheless very rewarding).

The puzzles are "amazing" because usually the answers are not what you'd expect.