#1 -- Lumines
Few launch titles have aged as well as Lumines--an addictive puzzle game eith a dynamic soundtrack that few players who picked up the game could ever forget. The gameplay maintains its frenetic but simple time-based block-matching at all times while the audio and visual style radically shift after clearing a certain amount of bricks. Each round had it's own style and every PSP owner deserves to play them all.
Full disclosure: AJ Glasser was a QA tester on Size Matters during the pre-Alpha stage.
#2 -- Ratchet & Clank: Size Matters
This is the first game from the Ratchet & Clank series that ever hit the PSP -- and it didn't just hit it, it rocked it if Metacritic scores are any indication. The game was mostly an adventure on the same scale as any of the console games, with several mini-games thrown in for good measure. The whole game came together nicely on its own, but because of the fully-voice dialogue and the attention to detail in the story, Size Matters felt like so much more than just a "PSP spin-off."
#3 -- Crisis Core: Final Fantasy VII
When it comes to spin-offs, this is the best you can hope for; a fully-voiced, richly-CG'd game with a smooth control scheme. Sure, classic Japanese role-playing game fans might cringe at the lack of turn-based or party-oriented gameplay (and the part where the main character isn't Cloud). But the action/adventure format made the battles fun and the cutscenes were sexy -- a definite must-own for the PSP.
#4 -- Tekken: Dark Resurrection
Every console deserves a good fighting game, and Dark Resurrection was definitely it for the PSP. You had a full lineup of classic Tekken characters, 19 stages to choose from, and the combos -- even if they were little wonky -- worked like magic. Even better, the game featured character customization, which is a great time-waster for handheld games.
#5 -- Star Wars Battlefront: Elite Squadron
Star Wars Battlefront games are pretty high caliber on any system, but the latest addition to the PSP's lineup of Battlefront titles introduces space-to-ground layers of combat for twice the fun in multiplayer. If you've got a lot of friends to play with and for some reason you're not into the Monster Hunter games, Elite Squadron should definitely be on your PSP-games-to-play list.