My favourite online games, most of which involve visuo-spatial perception and reasoning. All have >20 levels, each of which has a different puzzle to solve (unlike, say, the many variations on Tetris and Bubble Bobble), and start very easy then ramp up the difficulty later.
It so happens that I do think they are of educational value, in that visuo-spatial problem-solving is an aspect of mathematical thinking. However, mostly I like them because I just find this sort of thing fun.
Some of these are hosted on several sites, so if a particular link stops working, just run a search. Most are in flash, occasionally java. I’m running them in Firefox on either Linux Ubuntu or Mac OSX.
WARNING: If you’re still playing after the first few levels of any of these, you’ll probably be hooked. They are very addictive to a certain type of brain.
Blix (Edit: This game seems no longer to be hosted on Shockwave, or anywhere else, and searching for it just leads to a more recent (rubbish) game of the same name. NOOOOO! If you find the original anywhere, please send me the link! It has bouncy balls that you have to get into cups.)
Continuity (Edit: Free version of this seems to have gone, but there’s a downloadable smartphone/tablet version for under £1.)
I’ll add more to the list as and when I encounter them.