Truer words have not been spoken

Wind Waker anyone?

gameplay > story, characters > graphics

It depends on the game.

Many games such as New Super Mario Bros., Super Mario Galaxy, Super Smash Bros., F-Zero, Mario Kart and Pokémon don't need realistic graphics to be great. Fun gameplay and level design is what makes those game classic. Other games such as Metroid Prime, Dead Space and Skyrim rely on realistic looking environments to create a more immersive experience. (Which is why Metroid Prime 3 felt horribly outdated to me.) And then there are the hybrids like Halo, Call of Duty and The Legend of Zelda which kind of rely on it, but it isn't essential.

Or at least that's my view.

I'm probably one of the few PC gamers who's not a "graphics whore". For me graphics are just like a bonus for a game, if they look great then cool, if they don't, well as long as the game have great gameplay and story I don't mind the graphics at all. Art style is more important imo. 

It doesn't affect which system I choose; I spent most of my time this gen on the Wii despite owning the graphically superior 360.

Art matters more than tech for me; hence why I'll take the visuals of Muramasa, Kirby's Epic Yarn, Metroid Prime 3 or Super Mario Galaxy over Killzone 2 or Resistance 3. Heck, I still think Okami on the PS2 and Yoshi's Island on SNES look beautiful.

Graphics make up maybe 10% of a game's value to me, with gameplay taking up around 80%. I've loved plenty of games with not-so-hot graphics, like Skyward Sword and Goldeneye Wii. On the other hand, if the gameplay's not up to snuff, I don't care how pretty it looks. (Heavy Rain, FFXIII, Sonic and the Black Knight, Metroid Other M)

Graphics are what make a video game a video game.

Gyahahaha, I guess that's true. But still, look at the AI from good old games and you'll see we didn't have MAJOR improvements. I also could include Far Cry (was released before the HD consoles, AWESOME AI) or F.E.A.R (at the beginning of the last gen, best AI in ANY shooter I've seen yet). My point is: you don't really need OP consoles for a good AI, just good devs.

FUCKING YES! Graphics matter more now than ever! I'm  fed up with multiplats on consoles, I want better looking games, while PS3 exclusives still look amazing I want better hardware to go with it!

I think that it's rather naive to suggest that either graphics never matter or that they matter for all games.

I don't think anyone here would argue that graphics improvements would matter for, say, Tetris. On the flipside, graphics improvements for Endless Ocean would make a significant impact, since the graphics are one of the major points of the game (in a rare case of that being a good thing).

In the majority of cases, graphics that are "good enough" are sufficient. If Super Mario Galaxy had had graphics comparable to those of Super Mario Sunshine, or even Super Mario 64, it wouldn't have made it a worse game. N64 graphics are good enough for a game like Galaxy - any more is just icing on the cake, nothing more.

On the other hand, Dead Rising: Chop Til You Drop was a demonstration of a situation where graphics were not good enough for the game, and the comparison with the original versions emphasises this. The insufficient graphical power meant that the game couldn't provide the same experience, it was forced to provide an inferior experience.

Why did Pokemon only just move into proper 3D graphics on handhelds? Because it's only with the 3DS that the graphical power is sufficient to do the game justice. However, improvements to the graphical engine beyond this would be unnecessary - nice, but unnecessary. They wouldn't really matter.

At least, that's my opinion on the issue.

Poor graphics rarely prevent me from enjoying an experience but good graphics definitely enhance most experiences, especially with the type of games I like to play. I think this is the case with most people.

Everyone who says they don't care about graphics will go ape shit when a franchise they love comes out with stunning visuals (Zelda HD). As Visuals are one of the key components of what a game is, its unquestionably affects how you experience the game.