A portable game shouldn't be daunting to pick up. Nor should it become immediately boring once you've done everything.
Fun Action/Adventure games
Easily digestable RPGs. Trim unneccessary dialogue, concentrate on making the fighting/levelling/collection fun.
Racing games are okay if they dont become boring after unlocking the tracks. Burnout Legends style is the way to go!"
Competitive / Party games - especially single cart or online
"Non-games" (any software usually labelled with this might actually be a fun game after all)
Puzzle games
Music / Art games
FPS & Shmups (again, especially if single cart or online)
Point & Click Adventures FOR NINTENDO DS ALREADY!!
I'm thinking there of 2d/3d platformers, Zelda style adventure games, hack and slash games... racing games that get inventive with their tracks, or have loads of modes... Mario Party, Super Monkey Ball, Fusion Frenzy, Wario Ware Mega Party Games... practical PDA style software/applications you might use as a part of your everyday life, brain training software, or Nintendogs
... Soduko, Tetris, Lumines, Meteos, one line puzzle etc... Goldeneye 64 type software, Metroid Prime Hunters... DAY OF THE TENTACLE / SAM & MAX / THE DIG / INDIANA JONES / MONKEY ISLAND / #!~?!!
I'd also buy Pictochat-like software and spend a shitload of time using that if it went online. Sad but true.