As far as graphics are concerned, games in general age like milk. Nearly all games look outdated in five years... most in less and a select few somehow manage to still look pretty good a little longer than that. Gameplay, on the other hand, is a lot less predictable. Some gameplay feels dated a year later, some never does. It varies to much to make a general statement on whether games age well. Some do, some don't. I don't think you can even make a general statement on a genre. To me, Doom feels like it's aged better than... oh, let's say Halo CE. Same genre, but I can play Doom without ever thinking that it feels old. It just feels like Doom, and that's it.
There are other things that make a game feel old, though. A personal example that comes to mind for me is Command & Conquer. The very first one. It's very hard for me to play it now because I become frustrated at my inability to do certain things (e.g. assign a group of units to a number key). It does indeed feel like it's aged poorly. It's a problem with the interface. C&C Red Alert doesn't have better graphics, has only slightly different gameplay, and is only a year newer, yet it doesn't put me off simply because it has these interface features that are now expected of every single RTS.