I'm going to preface this by saying that FFVII goes without saying so I'd rather list some other games that I like as well. These are in no particular order.
Ico: If you want mind blowing puzzles and a truly involving world this is the game for you
Toe Jam and Earl Panic on Funkatron: Hurray for the Genesis days. What more can you want than to be aliens trying to expel a human invasion by bottling them up in jars while looking for food and presents to a funkadelic soundtrack.
Diablo II: Damnit I think I need a refund from blizzard for all the time I've wasted in their games.
The Fable series: British humor is awesome especially when it involves ruling a kingdom, procreating, or just being a jackass.
Katamari Damacy: Never could anything before it make cleaning everything out of a room so fun.
Honestly though this list probably changes on a weekly or daily basis. Of newer games I have to say I'm also really addicted to Assasin's Creed and just about every music game ever created.