Ah, Graphics. The vast majority of you will spend as as much (or more) money here as you will on any other single part of your build. That's a good thing, most games these days demand more from your graphics hardware than they do from anything else in your system. If you want to encode/transcode video, or edit photos, or render 3D graphics, you need CPU horsepower. If you want to game, you need just enough CPU not to hold your GPU back.
When recommending a gaming PC build, I generally advise a CPU/GPU combination with at least a 1:1 ratio in terms of expense. For example, if you're going to run an i3-2100, I'd recommend at least a Radeon 5770/6770. If you're going to run an i5-2400, I'd recommend at least a Radeon 6850/nVidia GTX 460 1GB. If you're going to break with that ratio, do so in favor of the GPU. That is, go with an i3-2100 and a 6850, not an i5-2400 with a 5770. Don't worry about your CPU bottlenecking your GPU, even a relatively lowly Core2Duo can still crunch enough numbers to avoid restricting most modern GPUs. More recent budget processors are significantly more powerful, and even less likely to restrict your graphics hardware.
With all that said, it wouldn't be a GPU discussion if we didn't cover what I'm going to refer to as "The Ever-War". Since what seems like the dawn of time, ATi (eventually bought and then absorbed by AMD), nVidia have been battling it out over the graphics card market. The conflict has caused some collateral damage to less worthy combatants (3dfx, Matrox, S3...) but serious competition has bred serious horsepower. The current generations of AMD and nVidia cards are well matched, relatively efficient, and impressively powerful even at lower price points. I would advise prospective buyers to leave their biases at the door when choosing hardware here. I've heard complaints about nVidia hardware, ATi/AMD drivers, and on and on. What it boils down to is performance, choose the best performing hardware you can afford. If you're looking at comparable AMD and nVidia cards, find out which one does a better job running the games you want to play.
In my recommendations below, I've highlighted what I think are some of the best options at various price points. Where possible I've included both AMD and nVidia options. At times, there is simply no comparison, and you'll only see cards from a single manufacturer. Prices are mentioned only in general, as video cards come from various manufacturers in many different models, and go on sale frequently. I've noted some cards that seem to frequently price drop into a different range where necessary to make sure people are on the lookout for good deals.
~$125 - AMD Radeon 5770/6770: This is really the only option at this price range. Nvidia's competition, the GTS 450, simply isn't as good as the 5770. The 6770 is a cynical OEM rebadge of the classic 5770. If you can find it for a comparable price to the 5770, go for it, but there's really no difference between the cards.
~$150 - AMD Radeon 6790 / nVidia GTX 460 768MB: These two cards run neck and neck, generally, and which you choose comes down to specific game performance and price. Keep in mind that, depending on sales/combos you might be able to find either the 6850 or 460 GTX 1GB for around $150.
~$175 - AMD Radeon 6850 / nVidia GTX 460 1MB: Much like the $150 category, both of these cards have very similar performance levels, and the differences are largely in whether a particular game was designed in such a way as to favor one manufacturer over another. One significant difference is that most 6850 models require only a single 6-pin PCI-E connector, whereas the 460 1GB requires 2 and is more power-hungry in general. Keep that in mind when purchasing. Also, do not buy a 460 GTX SE, it's a lobotomized budget model of the card and isn't worth your money.
~$200 - AMD Radeon 6870 / nVidia GTX 560: The GTX 560 is generally the better performer over the 6870. Not by an excessive amount, necessarily, but it's a more clear definition than at the $150 or $175 price levels. Fortunately, the 6870 generally goes for less than the GTX 560, which makes the value comparable.
~$250 - AMD Radeon 6950 1GB / nVidia GTX 560 Ti: Here the 6950 1GB is the superior performer. The 560 Ti is a good card, and can often be found slightly cheaper than the 1GB version of the 6950. Either card is a good value, and both have similar power requirements.
~$350 - 2x AMD Radeon 6850 / 2x nVidia 460 GTX 1GB: Sometimes the best graphics card for the money is 2 of them. Crossfire and SLI are no longer immature technologies with limited support and poor scaling, these days any game worth its salt supports both of these multi-GPU solutions, and scaling is very impressive. These setups offer GTX 580 levels of performance for a significant discount, even when you consider the expense of an SLI/Crossfire capable motherboard. If both the 6850 and the 460 GTX 1GB are selling for roughly the same price, the 6850 CFX is the cheaper option, due to its lower power requirements. If you prefer a single card option, then look at the GTX 570, the GTX 560 Ti w/ 448 Cores, or the Radeon 6970.
Options on the low and high end: Lower end GPUs are numerous. Let us know your intended resolution in order for us to offer the best price/performance option. Higher end GPU setups are largely a matter of deciding how much you're budgeting on the GPU(s) and then purchasing the appropriate multi-GPU setup (~$400, 2x 560 GTX / Radeon 6870, for example). It's generally not worth it performance-wise to go with a single card vs. a similarly priced SLI/Crossfire option, unless you have some kind of space/PCI-E slot restriction that demands it, or you intend to upgrade down the line to a SLI/Crossfire setup. Be realistic about the latter option, many times that impulse goes by the wayside, or you wait too long to drop in the 2nd GPU and suddenly you're better off just upgrading wholesale.
Recently, we've seen the release of AMD's Radeon 7970 card, and some of the lower-end derivations of their new platform. The 7970 is a fantastic card, the best single-GPU card out there, so if you're in the market for speed, and price is no object, there's no better option. The rest of the lower-end cards have begun trickling out, starting with the 7950 (another great card) and the 7770. Pricing is a bit off at the moment for the latter, as it's a bit more expensive than the 6850, but a bit less impressive. Once prices stabilize and the range of cards is closer to completion, you should expect to see the above recommendations change, at least on the AMD side. Kepler (NVIDIA's next big thing) is likely a month or more away.