Oh man, collecting obscure gems is my hobby. I go to gameshops to scour the used game racks. Some of my faves are Space Channel 5, Katamari Damacy, Ico, Tenchu, Soccer Slam, and Phantom Brave. My crown jewel at the moment is Rez, while my list of titles to watch out for includes
Ys: The Ark of Napishtim, Dark Cloud 2, Ghost Master, Okami, .hack, Bombastic, Mojo, Flipnic, Culdcept, Disgaea, Bard's Tale, Shining Force/Tears, Stella Deus, Freaky Flyers, Robot Alchemic Drive, Jade Cocoon 2, Samurai Jack, Shadow Hearts, Grandia, Okage, Dog's Life, Finny the Fish, Ecco the Dolphin, Escape from Monkey Island, Aqua Aqua, Chulip, Mojib-Ribbon, Magic Pengel, TransWorld Surf, Seaman, Super Farm, Mr. Mosquito, Jak3, Rachet and Clank3, Sly2, Tak, Psychonauts, Zapper, Amplitude, Gitaroo-Man, Kinetica, Yanya Caballista, Red Dead Revolver, Marvel vs Capcom, Zone of the Enders, God of War, Mark of Kri, Rise to Honor, Goblin Commander, Army Men RTS, La Pucelle, Twerps, Battlestar Galactica, Romance of the Three Kingdoms, Sphinx and the Cursed Mummy, Spy vs Spy, Powerpuff Girls, Piglet's Big Game, Asterix and Obelix, Theme Park Roller Coaster, Metropolismania, Super Monkey Ball, Viewtiful Joe, Under the Skin, Ribbit King, Crazi Taxi, Cel Damage, Simpsons: Hit and Run, Fatal Frame, Lego Star Wars, War of the Monsters, Destroy All Humans!
Note that, while most are, not all of of those are obscure. Also, I'll buy any obscure game if it's cheap, even if it sucks. Thus, a number of those titles are crappy games. Oh, and this is a PS2-centric list.