This is a very incomplete list of games to test with if you want to debug a specific feature. Hopefully you can find one that you own.
OS and hardware features
OSK (On-screen keyboard)
MotoGP (single-language)
PES 2013 (single-language)
Many more
Microphone (hardware expansion)
Invizimals
Infected (Shouting into the mic pushes enemies back)
Rock Band Unplugged
DJ Max Fever
Talkman
Go Explore
Camera (hardware expansion)
Invizimals
EyePet Adventures
GPS
?
GE rendering features and/or techniques
Spline/Bezier patches
Loco Roco (all games and variants)
Pursuit Force (both games)
Puzzle Bobble Pocket (completely unnecessary! Just used for rotating sprites)
Namco Museum: Battle Collection (Pacman, more). This still exhibits a small bug (black patch on top of the ghosts)
One of the snowboarding games
Vertex culling / guardband
DTM Race Driver
Race Driver 2006
TOCA
Vertex skinning/bones
Crisis Core
Tekken 6
Tekken 5
God of War (both games)
Many, many more.
Vertex morphing
Outrun 2006 (flame rings in 4th level on the left, 4 morph weights IIRC)
Motorstorm (vehicles, 1-2 weights only)
Depth buffer reads from the CPU
Wipeout (sun lens flare). Multiple reads per frame to get an average.
Syphon Filter (light halos (lots per frame!))
Midnight Club: LA (sun lens flare)
A few more
Direct color buffer reads from the CPU
Motorstorm (light adaptation)
Dangan Ronpa, Dangan Ronpa 2 (renders a separate mini buffer to select clues, people)
Coded Arms: Contagion (reads a single pixel from the alpha/stencil channel to identify enemies to lock-on)
A few more
Color buffer format aliasing
Outrun 2
Split/Second
Spongebob
Cars Race-o-rama
Depth buffer manual swizzling through geometry
This is a mistake that a few games have made - the PSP has hardware to swizzle depth buffers to linear, but instead they use triangles. This applies to the particle effects in these games
Ratchet & Clank (both games)
Jak & Daxter
Tricks requiring dual source blending
Wipeout Pure (bloom effect)
Armored Core 3 (issue #11430)
Lens flares in Ridge Racer
Intra-buffer block copies
Tales of Phantasia X/Cross Edition (included as a retro game in Tales of Phantasia: Narikiri Dungeon X). See issue #21098
Block copies to RAM, later used as texture
Digimon
Burnout Legends (sun lens flare)
Tales of Phantasia X
Memcpy framebuffer download/upload
Everybody's Golf 2 (line by line, ugh)
Zipped PRX
Fired Up
Persistent render targets
Mahjong Artifacts (mini) relies on render targets sticking around.