GB/GBC: The Legend of Zelda: Link's Awakening DX, epic adventure that you can take with you on the bus to school, or on road trips, also one of the best 2d zelda's (second only to A Link to the Past). Also features one of the best overworld themes (Tal Tal Heights) in the series.
GBA: Final Fantasy VI Advance, but for a Non SNES Remake, Metroid Fusion. Final Fantasy 6 Advance is a great port (aside from the downgrade to sound quality.. man that SPC 700 was so good when you go back and compare it to handheld sound, 8 bit sound, and the sega genesis.. heck I might even prefer the SPC 700 sound to what the PS1 had. Sorry for offtopic there, anyway, good port, with extra content, on one of the best games ever made. The story and gameplay lose none of their potency even though it was over 10 years old when they made the port. Metroid Fusion I like for it's super metroid style, and being a portable super metroid like experience at that.
DS: This is kinda a toughie. So many good games. So many good remakes on top of good original games as well. Chrono Trigger remake is great, as is DQ5, and FF3 and FF4. I know I'm going to get trolled here but I'm going to say my favorite original game on the DS is The Legend of Zelda: the Phantom Hourglass. Yes the temple of the ocean king and forced stealth elements may be annoying to some players but I felt they added some challenge, and I liked the way the stylus was used, a better rolling mechanic could have been put in place and I think the options to use the Dpad to move would be nice, but I liked the bombchu, hookshot, and boomerang use with the stylus.