I don't place too much emphasis on graphical fidelity, but I certainly do place a great deal of value on overall asthetic design. A game with a high polygon count or a super-detailed textures does not automatically make it better looking. Good art design goes much further than this, and quite often helps the game age significantly better than games which are built around a high degree of fidelity. Games which make use of sprites have continued to improve in quality since the 16-bit era (a lot of little touches have been added for the most part), but for the most part they don't have to look much better than they were at that point. They're timeless at this point, they'll never look bad provided the art design is up to snuff; many of the re-release ports from that era are either complete overhauls (Final Fantasy IV) or largely untouched (Chrono Trigger).
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To look at some of the more modern titles, art design is still superior to raw graphical detail. Here's a few examples of what I feel are the best looking titles in the past decade or so of gaming:
Castlevania: Lords of Shadow
This game is underrated as a whole in my opinion, but few can deny how great this game looks. Yes, it has a very high level of fidelity; it's not uncommon for the game to buckle under the strain of it's own ambition at times (particularly the Xbox 360 version). Nevertheless, it's a very colourful game (except the parts of the game which are supposed to be a wasteland) which makes great use of all the fidelity it's given; while other hack & slash games are also much better looking than your average shooter (argh, so much brown), they actually end up looking somewhat bland besides LoS. Not only that, it's significantly longer than games within the same genre; a bit more than double the normal length for the genre isn't an unreasonable estimate, meaning that many more beautiful vistas to see.
Final Fantasy XIII
Another game which gets more dislike than it deserves (again, in my opinion), though the flaws in this one a bit more pronounced than CV:LoS; both games take much longer than they should to hit their stride, but they're actually quite good once they do. But we're talking about asthetics here, aren't we? Say what you will about the rest of the game, but Square's art design is still one of the best in the business. Again, we have a very high degree of fidelity; again, it's another game which puts it too good use.
Shadow of the Colossus
Previous console generation, copious amounts of brown colours, loves bloom lighting (... I think); despite all that, this game still looks great. I'm not referring to the somewhat recent HD remake either, the original still holds up fine. As I said, it mostly comes down to art design; in the case of SotC, the minimalist approach works fairly well. Detail work didn't play a huge role in this game, but overall shape and scale certainly did. While many are quick to criticize colour palettes which are predominantly brown, this is a game which isn't hindered by it; perhaps proof that a lot of brown isn't necessarily a bad thing for a game's asthetics, even if most have no idea how to use it.
The Metroid Prime Sub-series
The first game in the series impressed me with it's impressive level of detail, much of it shown through the HUD of Samus' helmet: rain droplets on this visor, lens flares, fogging up when going through steam vents, catching a glimpse of Samus' face under the right circumstances, and many other things. The second and third games of the sub-series are no different. The level of fidelity in all the games is superb, especially taking into account the fact Nintendo's consoles aren't known for being the most powerful consoles, which makes the next point all the more impressive: all three games run at a rock solid 60 frames per second. The first two examples above are known to struggle under the weight of their own fidelity, while SotC's minimalist approach means maintaining it's framerate isn't an issue. The Prime games look just as good, if not arguably better, and manage to run like greased lightning; even better, they age very gracefully.
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Now, the question of whether graphics (or even overall asthetics) are more important than gameplay is a different matter. An amazing level of detail will not make up for a game which is awful to play. The first two examples above may not be the greatest games, but they're certainly not bad games either; the challenge getting the rabid masses to not hop on the bashing bandwagon and be reasonable about their opinions. However, the latter two examples are quite renowned for being outstanding games; the fact they look greate is just the icing on the cake.
I personally don't feel that graphics are the end-all for me, and for the most part I only view them as an additional perk to a good game. I didn't get the PC version of Skyrim because it looks better, I got that version so I could enjoy the mods. Speaking of which, it's a good looking game... but the art design isn't overly impressive in my opinion. Back to the point, a graphics aren't critical to my enjoy of a game; however, they do hold more water than the opinion of those on the bandwagon.