Hmm....
Tha Creed(Assassin's Creed Series) I have every single game in the series, including PSP and PSVita, the rest are on PC. I love it. Playing through III for the first time, had to start over because my save data got corrupted...
Zelda. All of them. 'Nuff said.
Grand Theft Auto. I truly enjoy free roam, open world games. Only have SanAndreas and IV on PC, and all the portable versions.
Big name Fighters: I'm talking Soul Calibur(I Dreamcast & II NGC), Street Fighter II(SNES), EX3(PS2), and Super IV(PC), Mortal Kombat Series(and I mean all of them), Fatal Fury(which I for some reason am bad at), Tekken III(yes only 3), Samurai Shodown V & VI(because 5 is the only one with all the characters) and many more.
Finally, the Final Fantasy series. After beating VII and Dissidia012 a few years ago, I've decided to play through them all. I'm about to beat FFI.
I do play SO MUCH more than that, but the OP asked for five. So...there.
PS....Gods Eater 2 needs to come to US. That is all.