Untangle is a game where the goal is to untangle a geometric graph. The game starts with several connected vertices and the player tries to move the vertices so that no edges intersect. Sounds simple right?
Here's a video of me playing the first few levels of the game.
The game becomes challenging pretty quickly. It's fun and interesting until you hit the "EVIL" level. It becomes more about tracking and organization. The game could use a fullscreen mode.
I remember playing the game some time ago. I revisited it when I was trying to recreate the game in GeoGebra, but a little digging around and I find this paper by Bose, Dujmovic, Hurtado, Langerman, Morin and Wood linked at The Geomblog. From that post, there seems to be a version for iPhone called Planarity and several versions on the android market when you search untangle.
UPDATE: Here's untangle played physically and collaboratively by a group of people.