Eye of the Beholder, Lands of Lore 1, Monkey Island (no need for the new graphics, IMO). That sort of thing. Like others have said before me, mostly 2D pixel games in colorful VGA and with professional art direction.

Soul Reaver is awesome. I remember I played it on my PS1.

Breath of Fire 3 still looks great. Hell, most Sprite-based RPGs since the SNES still look awesome.

Square titles, Mega Man X series, Donkey Kong Country, Super Street Fighter 2, Kirby games, Aero Fighters Raiden and other shmups, Legend of Zelda: Link to the Past, and the list just goes on. SNES has really great looking games, probably the epitome of sprite-based games.

The prettiest old game I can think of is 1869:

http://www.lemonamiga.com/games/details.php?id=219

Tron 2.0 still looks good for a 9.5 year old game. Due to the art style of that universe it will probably be one of those titles that never looks too dated.

This is old?

I thought the exact thing when I saw the OP.

Guess it's time to start kicking the kids off the lawn or something...

Hmm three comes to mind, Castlevania SOTN, Curse of Monkey Island, Full Throttle.

Yes

I guess it's all relative :)

Meh, I never really had abundant cash at the time (don't now either mind you), so I hadn't played new new games, that was actually one of the few I purchased new. :) So it looked pretty good when I played it, although I haven't played it for a while now.

My list.

Crysis

Battlefield bad company

Halo 3

Rage

On a more serious side..

Baldurs Gate 1-2
Icewind dale 1-2
Fallout 1-2
Doom
Ultima Underworld
Command and Conquer Tiberian Sun
Halo Combat Evolved
Alpha Centauri

there's a lot more.. But I do not want to list them all.

As a rule pre-rendered 16-bit colour graphics and top-end graphics demos tend to age horribly.

Generally speaking, there are two kinds of games. Those that try to stretch the graphics hardware of the given era and those that create an art style for themselves. The former tends to age poorly, the latter generally ages very well.

If you look at the vast majority of PS1 games, they look horribly dated with their low-colour pre-rendered movies, low-poly, low-res textured representations of human beings. It's ironic that most of the games that look best on the PS1 are the 2D ones like Castlevania SOTN and Tombi. There are a few decent-looking 3D titles on the platform like Crash Bandicoot, but only because the art style could be easily depicted on the PS1 without making compromises.

I could cheat and say something like Flashback: The Quest for Identity or any other 16 bit 2D sprite based game but I will take the challenge of suggesting some 3D games that aged pretty well.

Well, here is my list:
Unreal
Unreal Tournament
Need For Speed III: Hot Pursuit
Blood (Surprisingly enough)
Crash Bandicoot
Spyro Series
MDK
Re-Volt
Driver: You Are The Wheelman (Ignoring the character models)
Descent 1-3 (Since most of the 3D models are ships/robots, they do not need to look TOO realistic)

There are probably more but those are the only ones I can think of since it is pretty hard to pick some 3D games that still look good today,