This has been kind of a tough topic to respond to, and I've been thinking over my reply for a few days now. While I think I get the idea behind TPG's original post, I don't automatically think of older games as having "bad" graphics, even ones that haven't aged all that well. For me, it's pretty easy to put myself in the mindset of someone playing the game when it was new (as, in many cases, I am replaying older games from my youth) and view it as a product of its time, faults and all.
That being said, I can think of a few examples, mostly from the early polygon era on 32-bit consoles. The main thing that threw me off of a lot of early 3D games were the models, themselves, particularly the ones for human characters. Proportions were often out of whack, and many animations were done by hand, giving characters an unnatural movement. Not that this made for bad games, just some strange-looking visuals.
The original Tekken comes to mind first. That OG GunJack model...
eeeek! 
Cutscene graphics weren't much better, either.
It's incredible how much of a better job Namco's modelers did between the first game and the second. The game still plays well today, though, and at the time, I wasn't knocking it. Once Tekken 2 and 3 hit, though, well... different story!
TPG also mentioned the garish color clash of some games. One game came to mind right off the bat - Assault Rigs!
Again, fun game, but yeesh, they were definitely reaching for that Tron look. Not sure if they got it or not.
Robotron 64 had some trippy, low-poly visuals, and a ravin' soundtrack to match. Fun game!
I also liked Tetrisphere. Some of those color choices, though...
And one more for the N64 pile, Paperboy. Hmmm... come to think of it, this was a pretty bad game...
The visual style from a bygone era I miss the most is, by far, pre-rendered graphics. I was huge on adventure games back in the day, and titles like Myst, D, and Blade Runner blew me away with their fully "3D" worlds. I think the original Resident Evil captures this look well, too, along with its sequels. I'm not the biggest fan of the Donkey Kong Country games, but I think they still look great today, 25+ years on.
I liked the original Alone in the Dark, too. I remember reading a review of it back in the day that praised the game and graphics, but also said it kinda looked like it came straight out of the "Money For Nothing" music video. Hard to argue!
As others have said, I, too, adore the look of early 90s DOS games. Mixing limited 3D graphics with high-resolution 2D sprites yielded some pretty impressive results back then, especially on a crisp, clean CRT monitor. While it came by a bit later, I always though the original Need for Speed really nailed this idea. The road and other cars were 3D, while the driver's view in the game featured a highly-detailed and well-animated graphic of the dashboard and steering wheel, all in high-res sprite graphics. It was a very convincing look back then, and playing the game again recently, I think it still holds up very, very well, especially given the time of its release. Some of the screenshots Stalvern posted used a similar visual style, with roughly half the screen taken up by a 2D cockpit view / instrument panel. I love it!
And to echo many of the rest of us, yes, I will always love those big, boxy 3D arcade graphics. Hard / Race Drivin' comes to mind, as does STUN Runner. Atari really had that look figured out in the early 90s, then Sega just took off and ran with it soon after. Virtua Fighter, Virtua Cop, Star Wars Trilogy - I love 'em all!
Love the Dreamcast for the same reason, as many of the games were arcade ports and featured the same high-res colorful graphics of the source machines. When I bought a Dreamcast port of an arcade favorite, I knew what I was getting, and knew I was in for a treat. Was just playing the OG Soul Calibur the other night, and dear lord, I'd take it over 99% the fighting games on the market today, hands down. 20 years later and it still plays like a champ.
Fun topic, TPG. It's bringing back lots of happy memories!
