Best handheld game?

DS Lite will play GBA and DS games, not Gameboy or GB Color games. The new DSi will only play DS games as I understand it. And, for the sake of thoroughness, the original DS is backwards compatible with GB/GBC/GBA games.

This aside, another option that’s available is system emulation. I won’t get into specifics, but generally speaking, the DS is able to emulate games for the NES, Super Nintendo, Gameboy, Gameboy Color, Game Gear, Sega Master System, Sega Genesis, and a few other systems. Doing this requires the purchase of a special cartridge and a memory card to store the files.

Many PSPs can do this without additional hardware, as long as you install custom firmware on the device. Once this is done, it’s able to emulate all systems the DS can, plus the Gameboy Advance, Playstation 1, and more. (Note that the newest units — in particular, the PSP-3000 and PSP-2000v3, currently lack this capability. Thus, if this is of interest, you might be better off finding a used unit and/or one that’s already customized. Unlike the DS, the process to install custom firmware can be intimidating.