I think some people are confused or at least not really qualifying what they mean by "aged well".
Some are clearly thinking along the lines of "What FRANCHISE has aged well" which leads you to things like Sonic which started off great but died during the 3D switchover and has tried to ressurect itself by madly using the very thing that killed it off, in the same way a medic would plunge a knife into a stab victim in the vain hope of reviving them.
What I think the original poster meant was what old games have and haven't aged well, as in standalone titles from the past, as opposed to the franchises or series.
I think Mario has aged superbly. The originals are still modern, you could even take Super Mario Bros, put it in HD and it'd still look pretty cool due to it's classicly clunky and now "cool" retro aesthetics. Certainly the main line of Mario games (in my opinion things like Smash Bros and Mario Golf/Kart etc do not constitute as proper Mario games, they are something else) are still as fresh today as they ever were. I believe Mario Galaxy will still look incredible in another 15 years time, simply because these are games which have always been about visual design, and never really about graphical power, unlike most games. The fact Mario games look nice without overloading your eyeballs with visual information means they are classic.
Gunstar Heroes is another game I would say still plays very well. As does Super Mario Kart, Super Metroid. The entire Zelda series of games are all still strong after all these years, with maybe only the original NES Zeldas now showing some real wear and tear. Chrono Trigger is still rather brilliant, having played it through recently again.
Yoshi's Island on the SNES is classic too. It was stunning when it came out, but that patchwork/crayon aesthetic just will not age, it'll always look relevant. I think LittleBigPlanet will follow in its footsteps, or any game that prides itself on artistic creativity as opposed to mapping realism. And the controls are universal - I could play it on a keyboard and still have loads of fun. Take Goldeneye - that looks rather terrible now, and plays like the old rusty shopping trolley of the videogame world.
Ico and Shadow Of The Colossus - still beautiful. Shadow Of The Colossus is still one of the finest examples of art (not just visuals, but sound, music, atmosphere, emotion etc) I've ever seen in any videogame.
Starfox 64 is still brilliant.
Tetris is still the daddy of puzzle games. It's the videogame equivalent of chess - timeless.
I played Sega Rally in an arcade the other day, with manual gears - still brilliant!
Golden Axe, although never that great, is downright terrible now. Truly awful, along with Ecco The Dolphin, Double Dragon, the old Ninja Turtles/Simpsons arcade beat'em ups and Streets Of Rage. They just do not cut it these days. Tired, old repetitive gameplay and really limited artistic appeal. Anyone that laments the loss of these games in the modern age has the rose-tinted specs firmly on, I'm afriad. Play those games again, I'll be amazed if even hardened fans would make it beyond the second level before feeling like calling it a day.
The Metal Gear Solid series has aged badly, due to the fact even the most recent incarnation is tied up in its own heritage and ancient control method and camera system. I find almost unplayable now and wonder why the hell I put up with it or even thought it it was brilliant the first time around. I loved the first and second when they came out, then better action/stealth games came out with more logical controls and just left Metal Gear in the dust. I just about got around Snake Eater's fiddly controls and stupid run-into-camera backtracking sections enough to enjoy the story, but couldn't warm to MGS4 at all. Instead I opted to just watch the cutscenes on Youtube just to see the end of the story that I'd got 3/4 of the way through. But I just couldn't play it, it felt so archaic and was just frustrating. I could have finished it, but I now genuinely dislike the controls. Games like Assassins Creed and Splinter Cell came along with their more logical setups and I've never looked back.
I'll tell you what never ages well - games that 'pioneer' a certain graphical technology. Recently there was a lot of games which "pioneered" normal-mapping, but they're already looking terrible because of the reckless nature of the art - Call of Duty 3, Quake 4 and Doom 3 spring to mind. They don't look half as good as older games like Half-Life 2 simply because they plasterred everything with ugly normal maps.
Another videogame genre which seem to age badly are racing games, which as I've said, are often used to show off a piece of technology but then are quickly surpassed and forgotten. I mean "proper" racing games featurring real cars and realistic locations, not the F-Zeros and Mario Karts which are less reliant on cutting edge technology. Is there anyone that would play PGR3 over PGR4 for instance? Is there anyone that would play PGR4 over GRID? And when the new Need For Speed Shift comes out - will anyone bother with GRID? These games seem to sell on the basis that they deliver the most cutting edge, flashy racing experience, so they don't last very long at all.