In no order, had a think about my personal favourites:
-MGS 1 and 2
-Any GTA title from GTA 3 upwards, though I believe the early ones are fun too.
Final Fantasy 7 and 9
-Shaolin, PS1. I'd play it now if I could, proof that gameplay means more than looks.
Sega - Quackshot, Sonic 1 and 2, Kid Chameleon, Golden Axe, Streets of Rage. Could name many more for this but don't want to make too lengthy a post.
PS2 - almost everything
Only got the PS3 7 months ago,but love Skyrim and Hitman. Playing GTA 4 for the first time too, in preparation for GTA 5.