Final Fantasy 4, 6, 9, and Tactics Chrono Trigger and Chrono Cross Parasite Eve (The first one. Second one sucked) Resident Evil 1,2,3,4, and RE: Code Veronica X (They started getting lame around RE5) Breath of Fire 4 (nice gem of an rpg that nobody talks about) Grandia (Never got around to finishing that one, voice acting makes my ears bleed) Legend of Dragoon (On my backlog of games to finish too)
Think that covers most of the older ones
Sig is currently under construction. Deal with it.
Kirby's Dreamland NES FF 7 (tho I won't replay it the 12th time, since I swore I'll wait till the remake) FF 8 every now and then, will play again in the future. Street Fighter 4 (5 years "old"); almost daily. Other games I've only played once again (FF6, FF9, FF10, CT, Persona and many many classics more).
Everyone else already said it, but four years is still relatively recent. How can you possibly think that's old?
Anyway, I routinely still play tons of games from the NES era. I started on Atari, but in all honesty, Atari has very few games worth playing -- especially for a single player. The game I come back to the most often though is probably Little Nemo: The Dream Master. It's actually even more engaging than the NES Mega Man titles, which is quite a feat. Amazing game with some very unique mechanics.