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Game Boy, Pocket, Color, and Advance
The Game Boy Series. These are THE systems to get when you think about handheld gaming. There is no alternitave (Game Gear was the only thing close, but it was a battery eater). Although many Game Boy games have been kiddie recently, there are still many others that are great. And even a couple of the kiddie ones are actually good, for kids.
If you believe I missed any really great ones, let me know.