Kind of like SpiroGraph:
http://patterngame.com/linesuperfollow.swf
Click on the buttons for different shapes.

Tim Tang Test:
http://www.timtang.com/ttt
The Longest and Hardest Online Puzzle in the World!

I know quite a few that will make you wish I never mentioned them. They're fun, they're free, they're 'adware clean', they're family orientated, and they have no business coming into contact with any frazzled parents dealing with teens and mortgages who can use that time better spent screaming and ranting and frothing at the mouth.

Anyone wants to know of them, ask. I need a fun project.

-asks-

That subject was hijacked, well not hijacked but started again here. I listed a few domains where there are great free games. (Not shoot-em-ups, more like puzzle games.)