For the beat-crazed puzzle fan... Lumines II (read our review)
With its beat-driven, block-dropping puzzle action, Lumines was the PSP's first killer game. The gameplay hasn't changed too much in Lumines II - players still arrange colored blocks into patterns, which are then wiped out in rhythm with the music. But this sequel ups the ante considerably, adding tons of new challenges, a sequencer that enables players to create their own tunes and even full-on music videos that run distractingly behind the action.
Packed with features and still addictive as hell, Lumines II is one game you can't go wrong with - assuming the person you're buying for has at least a passing interest in puzzle games, of course.
Second choice: Gunpey