Games you keep coming back to

[The New Kid]

...Um, what? People don't play these games over again to prove that they've completed them before, they play them again because they enjoy them.

Anyway,

Mega Man 2 (Bubble Man's stage theme)
Mega Man X (How fast can you clear it this time?)
Final Fantasy IV (Nostalgia and OMG MOON)
Final Fantasy VI (I want my Kitten Hood)
Star Ocean: Till the End of Time (Someday, we'll collect 95% of the Battle Trophies. Someday.)

Ya, but I never watch movies or read books a second time over unless I really enjoy them. Haven't found a video game that has yet to do such a thing.