I personally only collect/keep games I will play regardless if they're shitty, so I appreciate shitty games - they're good in their own way once you find their charm.
These are some games from my PS2 collection that are often considered shitty:
AeonFlux
Army Men: Soldiers of Misfortune
Future Tactics: The Uprising
Haven: Call of the King
King Arthur
Men in Black II: Alien Escape
Mission: Impossible - Operation Surma
NanoBreaker
Spawn: Armageddon
Speed Racer: The Videogame
Admittedly, and other than Speed Racer, I haven't finished any of these, but I really enjoyed my time playing them.