On DS don't forget trauma center and phoenix wright games (the Japanese justice for all has english language option), great games. Mario Kart is killer too.
But as a shmup fan, PSP has it all...
emus with fantastic games (arcade -either from capcom collections, mvs or cps2 mame ports optims, snes, pcengine SCD, genesis, msx)
Gradius collection is spot on arcade
Star Soldier is a real feast
Ace Combat X is fantastic
in future, Parodius collection (sexy parodius on the go!!!), twin bee collection (twinbee yahhoo is fantastic) and salamander collections are coming.
For adventures, you can play Lucas adventures on the go (Monkey Island 1,2,3 , Full Throttle, Sam and Max, Day of The Tentacle, Indy 3 last crusade & 4 Fate of atlantis, The Dig, Loom) you can play the other adventures supported by scummvm too. Genuine stuff, there is a very good port of the classic Myst (but chances are you already finished that one)
FPS wise, you can enjoy doom, quake, heretic, hexen, SOCOM or the recent Medal of Honor.
If you don't speak japanese, Puzzle games... Lumines I and II, Puzzle Bubble (the later one), Puyo Puyo, Lemmings, Mercury... I d put The gottlieb pinball collection in there too (i looooove that game)
Fighting games, Bleach 3, Tekken 5 Dark Resurection, Power Stone 1&2, SFA3, Dark Stalkers (you need a paddle addon for the later 2, the handling with the stock cross is not great for circular motions).
Platformers, well Ghouls and Ghost, Katamari Damaci, Daxter, Megaman Powered UP, Loco Roco, Lego Starwars 2 (DS version is horrid bug ridden uncontrollable, PSP ver is fantastic).
Military action with Syphon Filter, Killzone or Metal Gear Solid Portable Ops
Racing with Ridge Racers 2 (no need of the 1st with the second), Burnout, Wipeout Pure, Outrun 2 .
Sports, you got Fifa and Winning Eleven, Virtua Tennis, MLB 06 (i m not a fan of sports games). Haaaaaa i forgot one of my first games but i love it: Minna no golf ! (everybody s golf in english iirc)
Of course, lets not forget the 2 GTA games Vice City and Liberty City.
I could enumerate tons of examples of games worthy of owning a PSP (i have over 30 genuine games for it, and err... the whole rest of the library not so genuine :P).