Occasionally I will play an old game. I've plugged my way through Castlevania SOTN numerous times, Zone of the Enders 1 + 2, and this past year I went through and replayed Prince of Persia SOT, replayed and finally finished PoP WW, and continued to finish the series. I used to go through Legend of Zelda LttP quite a bit also when my SNES still worked.
I have a problem where I will play a game, but then move to a new game without finishing the first one. I have a number of games that I haven't finished (some I have barely even played), but with the understanding that SOMEDAY I will get back to them. Even some old PS1 games are on this list (FF8 and Tactics Ogre, I'm looking at you). Currently I need to get back to Stranglehold, Katamari Forever, Marvel Ultimate Alliance 2, Goldeneye 007 Reloaded, Sorcery, which is probably the most successful PS Move title in existence, Metal Gear Solid 2 HD (and then go into 3 and Peace Walker plus replay 4 ), and Borderlands 2. At the moment, I'm working on Assassin's Creed 3.
So yeah, I do replay old games, it's just hard to find time to do so when I've got so many other games to play. I'm getting better at making sure I finish a game before moving onto a new one, but when I'm really looking forward to a title, like AC3, everything else goes on the back burner.