I for one prefer to pirate the hell out of my games!
lmao just kidding
Anyway some favourites other than Godzilla games are:
Yoshi Story
Mario Galaxy
The original Halo trilogy (Special shout out to Halo 2: Anniversary)
Pokemon HeartGold/SoulSilver
Pokemon Alpha Sapphire/ Omega Ruby
The Sims 1, 2 and 3
TMNT Arcade games (And I'm looking forward to TMNT: Shredder's Revenge)
Tales of the Abyss
GEX
Dragon Quest (Just about any of em)
Metroid, Zelda, Nintendo, Nintendo, Nintendo LOL
Honestly I'll play about anything as long as its not the real ultra violent stuff, I just dont go in for that but it doesnt bother me if others enjoy it. Halo is probably the closest but its pretty tame compared to like Doom, Gears of War or something.