Been going through some of my old games recently...
Ones that have aged well:
-Starcraft. This game seems immortal. There's so much depth of play, the game is balanced to a tee, and there's a still a significant community of eight-year old Koreans who will happily kick your ass online whenever you want.
-Civilization IV. The graphics are still pretty good, the AI is smart enough to be interesting, and the higher difficulty levels are pretty challenging, and there's lots of depth and strategy available.
-Heroes of Might and Magic II and III. Unlike other sequels, I think both of these games have actually kept pretty well. Heroes III, I think is probably the best in the series; it's a beautiful, well-balanced game with an interesting and fairly challenging AI. Heroes II is just fun to play, and has a great campaign.
-Super Mario World. This is a bit of a weird one. Somehow this game has picked up a huge, dedicated modding community, which has really revitalized it. The mods take advantage of the fact that they assume everyone is using emulators where you can save anywhere you want and fix your mistakes easily, so some of the mods are fiendishly, comically hard. Look up Kaizo Mario... Or download Lunar Magic and make your own mod.
-Ancient Domains of Mystery. My favourite rogue-like. Always entertaining to play, very challenging and great depth. The game developer has recently taken it updating it after many years of inactivity, adding a bunch of new content and fixing some persistent bugs.
-The Incredible Machine. This game is just hilarious.
Games that haven't aged as well as I expected:
-Warcraft II. If you've played anything more recent, the game's poor AI will stick out like a sore thumb. Units constantly get stuck everywhere, and the computer AIs are predictable and have really obvious flaws (like sending all of their workers without protection to try to use your mines if they run out). Haven't tried to play online, but single player was pretty disappointing. The problem that humans and orcs are almost exactly the same, except that the orcs have way better magic and are therefore much, much easier, doesn't help either.
-Civilization II. Sort of the same problems as Warcraft II. The newer games in the series fix a lot of the flaws in this one (granted, some of them introduce new ones), so compared to the newer games in the series, a lot of things in this just don't work out quite so well. The game's extremely crude diplomacy system makes it so every game is almost the same: Get a decent lead, all the computers ally against you and declare war constantly until you kill them all.