Dino Run by Pixel Jam is a great game with an awesome plot - a meteor has hit the earth and you (the baby dinosaur) must run away, as fast as you can, from a fiery death and therefore avoid extinction! What else do you need? Great game play. Whats makes it interesting is that it looks like a video game from the late 80's. So basic and simple yet so appealing. Pixel Jam have a load more pixel games to play on their site.
Another guy who is doing some interesting things with pixel games is Mark Essen. His old school style games goes to show you don't need fancy graphics if you get the game play right. Most of his games have no real goal, and it's still okay, they are so therapeutic to play you don't mind spending the time. Zen games I believe it's called.