I will be listing here the online puzzles. Anybody can contribute to this topic by adding new links. Thanks!
http://www.magickeys.com/books/jigsaws/
http://www.dltk-kids.com/puzzle.htm
http://www.thekidzpage.com/onlinejigsawpuzzles/index.htm
http://www.puzzlehouse.com/_onlinepuzzles/onlinepuzzlesmain. htm
http://www.crea-soft.com/online-jigsaw-puzzle/puzzles-catego ry-8.html
Here's a list of the puzzles I remember off the top of my head. I'm on vacation so I don't have access to my bookmarks on my home computer.
http://www.flash-gear.com/puzzle/ - for making your own puzzle using an image on your computer. You can choose the puzzle piece size.
http://www.uptoten.com/kids/kidsgames-puzzles-wagonpuzzle.ht ml
25 piece train puzzle.
http://www.uptoten.com/kids/uptoten-features-search-searchpa geresult.html / click on the jigsaw puzzle category to find 20 other puzzles at the same website as the above train puzzle.
http://www.thomasandfriends.com/usa/building.html - 5 and 13 piece train puzzles. These are good beginner puzzles because the pieces are broken in logical places (by train part) instead of random places (like a jigsaw).
http://www.postmanpat.com/ - easy, medium and difficult levels. The child can do the puzzle with a blank screen, with shapes showing, or with the picture showing.
Scroll down to see lots of online puzzles. You can choose from 6, 12 or 24 pieces. Puzzles for art lovers, pirate fans and more:
http://www.mightybookjr.com/Catalog_Games.php