My first dedicated gaming system was the PS1, and in general I have no trouble going back to the sprites and chunky polygons of the mid-to-late 90s, whether on consoles or computers
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as long as I can upscale them to 1080P
Beyond that it gets a bit hit and miss- SNES and Mega Drive games look and sound fine to me and I've played plenty of 16 bit console games as an adult. On PC, I can enjoy 2D stuff like Sam & Max Hit the Road or the original X-Com but most early 3D, like the original System Shock, looks a bit too much like visual vomit.
Going to 8-bit, while the vast majority of NES games are too primitive to my eyes and ears, I have no problems with Game Boy/Game Boy Color games.
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(Well, at least the good ones, mostly made by Nintendo)
Is it just nostalgia because I had a GBC as a kid or is it because Game Boy games came later and had more developed visual aesthetics? 
My limit is probably the very late 80s
I mostly play older games via emulation, and the biggest issue is the rough transition from 2d to 3d graphics (PS1 and N64 mainly) that was smoothed out with the Gamecube and PS2 (and Atari 2600 garbage, I doubt anyone seriously played those classic collections). I think the PS1 especially jumped the gun with 3d, where stuff like Rayman and Symphony of the Night are really timeless. For the N64, I still really like Majora's Mask and Ocarina of Time.