I tend to find that if the game is good then i get absorbed in it and i don't notice the graphics at all. Even playing old games that haven't aged at all well, it doesn't matter if the game pulls you in.
though it does expose games that relied ONLY on graphics... those don't age so well.
I'm not sure i'd agree about the games that moved to 3D in the early days though. usually it was the GAMEPLAY that suffered in the transition, rather than the graphics.
I still think most N64 games look great. I'd happily play a lot of them. while i think a lot of the transitions to 3D at that time were a bad idea, driven only by bandwagon jumping... there is an undeniable "something" to 3D that draws you into the world.
Not for all games of course (chrono trigger rocks), but i found that time/generation was when i started getting drawn into the worlds that were created.. whereas a lot of the SNES generation was more about *playing* a game.
Can't think of a game i didn't enjoy due to only the graphics.

Well, one of my all-time favourite games is Secret of Mana. Released in 1992 for SNES, it still offers a lot of fun. The graphics are very good, though. It's too short and too easy, but apart from that, it's good. Yes, I admit: I like all of the SNES RPGs, but this is still my favourite one.
If they could make a game like that again, I'd buy it. And I wouldn't want a new fighting system like introduced in Seiken Densetsu 3, and I wouldn't want a more realistic or even any better graphics. It should be just that simple 2D isometric comicly thing. Shining Soul combined this with RPG elements to create a diablolike game and it also was quite good.
As Dale Schacker said:
Of course, when it comes to PC games, to the best I've ever played belong Day of the Tentacle, World of Goo. They have not great graphics? Maybe, but they have humor. I had a lot of fun with these. Graphics doesn't matter if a game is good.
And I still play Commander Keen and those old Apogee Jump'n'Runs sometimes. The graphics are bad compared to today, but the games are top. I also have Duke Nukem: MP on a CD and liked it very much. Good graphics don't have to be a bad thing if the gameplay is good. ;-)

System Shock 2:
yes, i loved every moment of the game, and the rendering of the environment/mechanical stuff is good enough, however all human models are absolutely awful, even compared to the low-poly standard of the time. (all the human models in Quake II engine based games, for instance, were by far better looking)
Even worse is how they look in the few pre-rendered cutscenes, including the ending one, what a letdown!
Heroes of Might & Magic 3:
I really liked both the gameplay and the art stile of chapter 2, and while HoMM 3 is a superior title in every aspect of the gameplay, the new graphical style, while on the surface more detailed, looked instead very confusing, grainy and dull.
Proof:

You need to play more 3D games. OFP may not be the prettiest girl at the party but she'll do things for you that the others wouldn't even dream of. Sure she has issues but at least she's not superficial and riddled with bugs like her prettier younger sister ArmA

I never said the game was bad, just visually inferior. But there are many early 3D games I've never had the chance to try, which I'm sort of trying to make up for now.
I did try ArmA once. I never got past the chopper training, because the retard that was going to enter the chopper with me, never managed to walk around the damn thing to enter it.

Alone in the Dark.
Great backgrounds, but horrific looking 3D models.
Cutting edge at the time, and I do love that game. Unfortunately we only got three games in that series. ONLY THREE. (actually I'd shorten that to two games, since the third just wasn't up to the same standard imho.)
I remember having an argument with someone about Starfox back when that first came out, I essentially said it was ugly and no better than Elite Plus, he thought it was the second coming just because it was 3D.

Darklands had horrible graphics but the gameplay was so damn awesome you could kind of forget about the graphics and enjoy the free roaming nature of the game...well until your party got too old for adventuring. I can guarantee you will never play the same game twice!

http://drog.terra-arcanum.com/highres.html#screenshots ;)

I always loved a game called "SOS The Final Escape" (aka Disaster Report in US) on PS2.
Technically, the game is just horrible. Graphics, without being awful to watch, seemed so old at its release. Controls are horrible, as well as the camera. The story and the characters are very classic, I'd even say badly written. The game is very linear and scripted, etc...
But, I must say that the immersive aspect and the overall atmosphere in the game is just great, very well done. You really have the feeling to wake up in a town destroyed by a natural catastrophe, it's really a pleasure to evolve in it.
The only thing that drives me crazy: the game originally takes place in Japan, but for US and UK, the game has been occidentalized (not sure about that last term...), all the characters in the game have... blond hair... just crazy.
The sequel, "Raw Danger", was not bad at all if you like the first one, but suffers from the same occidentalization (not sure at all about this term either...).

ugh. delta force.

Of games with really atrocious graphics, I'd go with Hellnight (ps1) or Clock Tower (ps1). Hellnight was an extremely obscure Japanese and Europe only first person survival horror game by Konami/Atlus that was absolutely brilliantly done. The wall textures look like something out of Doom 2, though. The graphics in Clock Tower are honestly just terrible, but it's one of the best survival horror games I've ever played in my life. They didn't really update he enine much from the SNES game that came before it.

Ah! The majesty of Voxels!
Why didn't they ever catch on...

5 games... alone in the dark 1-3 plus new nightmare and alone in the dark (why they would give a game that isn't a remake of the first the same title when they already had a subtitle picked out (near death investigation) i'll never know)

The other 2 don't count ... there were only 3 AITD games...