What the heck. I just wanna put clothes on.
I never think about graphics in a game, at least not technically... how many colors, bump mapping, textures, all that crap I really don't care about.
What I care about is character design, interface design, how the graphics work together with sound to create an atmosphere.
I care about a game's style.
Whenever people think of style, they're immediately drawn to cel-shaded or with an apparent stylistic approach--like the above game, "The World Ends with You." It's got a grungy look to everything; the menus, the fights, the enemies, the graffiti, the city... and it has a really funky soundtrack too. All of this makes it pretty trippy to play, which is a good thing. I can think of a number of other games that come to mind too--Wind Waker, Okami, No More Heroes as games with "style." Of that list, I only played Wind Waker which did actually look really cool, but suffered from a few gameplay flaws.
It's not always about crazy cel-shading or purposely injecting the artsy look. One of my favorite stylistic games was Gears of War. Sure it's got a shitty story but I love the atmosphere. You got troops that look like they're on steroids spouting bad lines, and there's the massive bloody skirmishes with aliens. The gameplay systems like the cover system, the roadie run, and the diving and rolling made it feel chaotic and crazy. And yes, this game had all that technical graphics crap done to it.
One of the main reasons I favored Tekken over Virtua Fighter was because of how much better it was stylistically. Whenever you hit someone in Tekken, there's always some crazy graphical effects... explosions, fires, blood spatters, blue sparkles, electricity whatever. And each fighter had a signature graphical effect too. Compared to Virtua Fighter, when people hit each other, there's no graphic effects, yet they still have the same juggle combos, so it's kinda half-assed realism. And then soundwise, when people get hit in VF it sounds like an earthquake but again, there's no matching graphics, just people getting hit and nothing to really show it.
I used to love the Gran Turismo series, and it's been getting closer and closer to photorealism, but I feel that t's still lacking in atmosphere. If I get to 100mph in my car here, it feels ultra fast. (Maybe because Toyota Camrys aren't meant to go 100mph.) When I get to 100mph in GT, it feels the same as going 50 or 60. The only time I've felt like I went fast was in GT4 when I go 230mph on the Le Mans course where the slighest turn of the wheel makes you feel like you'd spin wildly out of control. Again, everything looks real. Everything sounds real. But nothing ever gets the heart pounding, the adreanaline pumping, the hands covered in sweat as the engines roar while you try and pass a car at 130mph on Tsukuba Circuit or grind out a long drift in rally mode.
I could go on and on and name a ton of games, past and present, that really establish presence and style... but I'll leave that up to you guys to debate amongst yourselves.