I love playing Descent. It's still great fun.

I feel like an asshole, I forgot the most obvious one. Not only has it aged well but later games in the series, while good, were never AS good. Of course I speak of the Holy Grail, Sim City 2K.

Anyone who refuses to play Zork is a terrorist.

You hear that NSA? Go get 'em!

Not sure if this question is referring to both gameplay and graphics, or just one or the other, but, still, here are my picks out of the GOG games I own, and some other titles I'm interested in but still hadn't had the money to buy:

Sanitarium (graphics look cool, gameplay-wise it's just your run-of-the-mill point-and-click adventure game, but the story... hell. Holds up today, will probably always hold up)
Planescape: Torment (do I need to say anything regarding this superb game?)
Beyond Good & Evil (not *that* old, but it shows what classic adventure games could have been, when adapted to modern audiences. It's a shame a sequel was never made, and that these kind of adventure games somewhat fell into oblivion)
Broken Sword series (at least the first two installments; those cartoon graphics were mind-blowing at the time, they still look pretty good today)
Psychonauts (not that old, I know; the graphics are quite outdated, by today's standards, but the art direction more than makes up for that; plus, when it comes to pretty much everything else, it's just stellar)
Clive Barker's Undying (just try it. Please. It looks old and ugly in screenshots and videos, but once you've played it... you'll know what I mean)
One Unit Whole Blood (amazing, classic early FPS unforgiving game, superb art direction -- even though you do have to be able to enjoy what devs made with the Build engine, back then, bearing in mind the game *will* look "bad" compared to, say, Half-Life 2, but its art direction is amazing nonetheless, and it shows what the Build engine was actually capable of)
Oddworld: Abe's Oddysee/Abe's Exoddus (probably the best puzzle platformers you could play on a PC; graphics do look old, but they still maintain the charm and "strangeness" we remember them for)
Nox (please, please, please: TRY IT! I hold this game in the highest regard. It came out before Diablo II and introduced some things that are now standard in action CRPGs/hack-n-slash games. Art direction is amazing, story is engaging and sometimes very funny, gameplay is as intuitive, enjoyable and fluid as they come)
Earthworm Jim 1&2: The Whole Can O' Worms (classic platforming fun, hard difficulty level, old-school cartoony 2D graphics, plenty of over-the-top humor. A lot of people don't know this, but the cartoon was the one inspired by the games, and not the other way around. Earthworm Jim had such a preposterous setting and was so greatly animated that they thought it would make a great cartoon. Which, in fact, it did. The games are better, though)

There are more, oh, yes, but these are the ones I can think of off the top of my head.

Psychonauts (if that's considered "old") is excellent all-around.

Duke Nukem 1+2 - Gameplay is very solid and enjoyable. If you need shinier graphics, then this might not be for you. I played them for the first time earlier this year and loved them both.

Disciples II.
Praetorians

Exactly. Is Psychonauts "old"? I listed it as well, but I couldn't help wondering to myself "is this game old?" Or, at least, "that" old... I've been playing video games since the NES days, there are people on these forums playing them since the Atari and ZX Spectrum days, so are these newer games "old", to us? I still remember when American McGee's Alice came out in 2000 and people were so concerned because it required quite a hardware upgrade to play, since most computers back then didn't meet the minimum requirements you needed. I recall how the graphics in that game were so ground breaking, something you had never seen before, and by the end of 2001 they looked really old and obsolete.

Now, excuse me as I go vote for American McGee's Alice on the community wishlist. If they have the great Clive Barker's Undying, which came out at roughly the same time, there's no reason for them not to have McGee's Alice as well. Both were published by EA, with whom GOG apparently is in good terms, so...

Of the games I own through GOG:

Sim City 2K- as mentioned by TinyE. I would prefer to see SC3000 as that's the better game (imo), but SC2K still holds up well as a city builder.

SM Alpha Centauri- As addictive as ever. Has maybe been surpassed in the genre. But still enjoyable.

Pirates! Gold- Being a swashbuckler never gets old. Pillage! Plunder! Woo the governor's daughter.....yarrrr!

Conquest of the New World- A personal fave. The graphics were outdated fifteen years ago. But the gameplay is timeless if you enjoy 4X games.

Patrician 3- Only if you enjoy trade simulators. If not, you wouldn't like this game in the first place. But if you enjoy setting up economic networks this is still one of the best out there.

Caesar, Pharaoh and Zeus games. Amazing games..

Infinity Engine games
Fallout series
Might and Magic 3-8 (ignore 9)
Ultima 7 (may not look good but it plays well)
Zeus and its counterparts (Caesar and Pharoah)
Painkiller
Evil Genius
Most of the Bullfrog games
Build Engine games
Carmageddon
HoMM 3 (only one I played to comment on)
Rayman series
Outcast
And many more

Pretty much anything with 2D graphics or 3D graphics after 2000-ish.

Thief.

I actually prefer the dated graphics even now to many newer games.

I was about to say basically this.