AARP Free Online Games - The AARP site has several good online games including a daily jigsaw puzzle. You can access puzzles from the past month with the selector at the bottom of the page. The puzzles require the ShockWave plug-in, but should work on just about any computer.
JigZone - JigZone has a great variety of puzzles with many choices for numbers and shapes of pieces. The puzzles should work with almost any fairly up to date computer.
Flash Puzzle Zone - As the name indicates, these are Flash based puzzles. There is a very large variety of images and you can even create your own puzzle by uploading a picture.