Okay, so this isn't about all kinds of puzzles---it's really about mathematical puzzles, and there's a focus on puzzles that I like (particularly wooden polyhedral dissection puzzles).
Binary Arts (now called ThinkFun)
Bart Buie's Stewart Coffin Puzzles
Cubic Dissection (also has forums and a gallery)
Tessellations and MathArtFun
Bill Cutler Puzzles, Inc.
Mr. Puzzle Australia
Puzzle Master Inc.