2. Flow Free by Big Duck Games LLC
I have had this game on my iPod for two years now. It was the only game I managed to teach my mother how to play (the whole touch screen thing was originally very jarring to her). I'm the kind of person that, if I enjoy a game enough from start to finish, I will erase my previous scores and replay the game. This is definitely a game you can do this with. Basically, the game is a series of dots on a grid that you have to connect, while filling all of the empty space on the grid and not intercepting lines. It sounds like a lot of other games, yes, but for some reason this one has stuck with me. There aren't any obnoxious characters cheering you on, no brightly colored backgrounds to purposely get you distracted, and just because you've completed a level doesn't mean you've passed it. There aren't five levels of stars you can achieve depending on your performance. There is one star. You get the star if you complete the level in the least amount of moves. Getting that star is really super rewarding.