Coincidentally, all my favorite PS2 games can be found on the hella cheap. All links goto ebgames.com. Game price at the end of each description in parentheses. Use code PPLAY15 to save 15% off of preplayed games at EBGames.
Space Channel 5: Special Edition: Includes both Space Channel 5 and Space Channel 5 Part 2 for the unbelievably low MSRP of $14.99. You know the score: simple simon says type gameplay, but fun nonetheless. I've seen it sitting around lonely and unloved for $10 at Target. ($14.99 new)
Victorious Boxers: A stylish 2001 boxing game with the Hajime No Ippo manga/anime license. I didn't know the first thing about the manga/anime when I picked it up, but just loved the hell out of the gameplay. Character movement is all analog (punches are buttons) and there are no lifebars of any sort. It's a great break from the EA type boxing sims. ($9.99 preplayed)
Ace Combat 4: Very fun jet-flying game. 5 is coming out this fall. ($14.99 preplayed)
Sky Odyssey: Underrated/overlooked PS2 launch game. It's all flight, no shooting, but is very enjoyable and engaging -- even if it looks like ass at times. ($8.99 preplayed)
Disaster Report: A unique survival type game where you don't kill enemies and your goal is to escape an island besieged by earthquakes. It's a little rough around the edges, but I really enjoyed the premise. There's a good amount of slowdown, but you have to be patient with it (12.99 preplayed, link goes to GameStop)
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EBGames says all their preowned PS2 games come with case and manual. Personally, all the PS2 games I've ordered from them have arrived in great shape with all the packaging. Never ordered from GameStop. With a little searching around, you can probably find them for better prices than the links given anyway.