Yeah, I tend to habitually replay games after beating them, and often stick with them for as long as a month or two, maybe even more depending on how immersed I am. I always play on normal first, then if there's something to be achieved at higher difficulties I'll give it a try, not always though. I like to do speedruns occasionally, so that's also a factor for me replaying a game. I'm quite competitive, too, so if a game has challenges, I won't drop it until I can get the best time/score possible.
These are some games off the top of my head:
Kingdom Hearts II
ICO
Shadow of the Colossus
Double Dragon Advance
Pokémon Gold Version
Final Fantasy VII
Final Fantasy IX
Final Fantasy X
Mega Man X
Sub Rebellion
Sin & Punishment
Pokémon Snap
StarFox 64
Pokémon Diamond Version
Kingdom Hearts 358/2 Days
Mario Kart DS
SNK vs. Capcom Card Fighters DS
Chrono Cross
Metal Gear Solid
TMNT (PS2)
Super Mario Galaxy
Bujingai: The Forsaken City - haven't gotten everything yet, though
Batman: The Brave and the Bold - The Videogame (NDS) - this is a rather easy game, and even though there's really nothing more to achieve once you beat it, for whatever reason I couldn't drop it for almost a week