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
visually old games are fine, but design wise they can get iffy for me. I'm sorry but random encounters just aren't fun, it stopped me from playing persona 2
its a problem in more recent games too. I've been replaying dragon age 2 but I had to put it at the lowest difficulty just because of the endless random encounters and waves of enemies. Its so frustrating.
especially when the encounters aren't brief, it's just awful. why can't we choose when to fight or when to stealth around an enemy?