I know it sounds like a knock-off to quote Extra Credits, but "graphics should be there to serve the asthetic." And for that matter, everything else.
Best example I can think of right now: Doukutsu Monogatari, AKA Cave Story. 8-bit graphics, but a simple platformer with a heart-wrenching plot line, lots of great characters and upgradable weapons. I liked this game more than the cookie-cutter stuff they kept churning out in that time, but I am a bit biased towards platformers, so cut me some slack.
Also, GTA San Andreas VS GTA IV... San Andreas hands down. Bigger map, more relatable characters, broader line-up of support characters, wider variety of missions based on setting, involving storyline... Yeah... I still enjoyed SA more than IV.
I would sacrifice graphics for storyline, good controls, realistic characters or innovative design choices almost every time.