The Nintendo DS was the first touch screen handheld gaming device from Nintendo. It followed up the Gameboy Advance and added not only touch controls with a stylus but a second screen, microphone and tilt controls.
There are a huge number of DS games that you can get at reasonable prices. They can be played on the original DS hardware as well as the DS lite, DSi and DSi XL. It has a local Download Play multiplayer mode where you can often download the game from one cartridge to many DS handhelds.