Where do you draw the line?

Depends.... when its 2D sprites... some SNES games are still pretty darn good looking imo.
When it comes to 3D?.... Wii level.

A new game today comes out, and it has worse than Wii graphics, I wouldnt find that acceptable, no matter how good it is.

3DS  is a handheld,... so im abit easier on that fellow.

For 3D - PS2 era (6th gen I believe) I really cant play most n64 or psone games now. The way they look repels me.
For 2D - Almost anything, really? Nes and Snes graphics are ageless for me.

Those FF7 character models :P

With PS1 it really does depend. I am fine with how FF9 looks as well, and other games like Breath of Fire 4 still look good. 

For 3D- Anything from 6th gen onwards. N64/PS1 graphics just don't look right.
For 2D- Anything down to the NES. Atari 2600 games might be a bit too simple sometimes.

depends on how you mean the question

if you're talking games released today that are ATTEMPTING to look semi realistic that don't look good... then that's an issue. if you're talking about overall taste- I love the look of a lot of simplistic stuff from the 8 and 16 bit era equally as much as stuff from today

its sort of in the same vain of why comic books never really look that 'dated' per say. Some art styles last. I would even argue that certain things in like the N64 era (despite the awkward transition to 3D) have a charming look to them because of the limiting technology forcing a sort of comical polygonal look to the characters and things (at lesat with the N64)

go back and play Spyro or Diddy Kong Racing or Banjo Kazooie or Mario 64 or Ocarina of Time. They look perfectly fine if you accept them for what they are. even in their time they were not going for insanely realistic graphics or anything but rather forcing a somewhat comical angle because you had to. I think that is a big reason why so many big franchise characters to tend to be cartoony, because they've been able to transition through time so well.

Obviously if you go back with a bad attitude and play something like Goldeneye you might find complaints because it was attempting to look as 'real' as possible during its time, but even then I don't think its that bad. People have this strange thing where they seem to automatically call anything squared or polygonal ugly and I disagree whole heartedly

Pretty much this. Okami holds up to this day, as do plenty of 8 and 16 bit games.

Depends on the art style they are going for, but generally, at least GameCube quality for 3D games so 6th gen?

Hard to say :/

Ps1 era graphics are as low as I can enjoy a game.  So spyro,  metal gear solid,  hogs of war,  crash bandicoot etc I can enjoy those games.