If you want to upgrade a cheap mass market desktop computer like a Dell Inspiron to play modern games at 1080p with details set to reasonable levels you'll need to find a graphics card that will work with the weak power supplies such systems come with. That, or replace the power supply in addition to getting a new video card. Many pre-built systems, like the Inspiron 546 model my cousin is using, come with 300 watt PSUs that won't support a high-end gaming graphics card. Fortunately there is a low-power option that doesn't need an additional 6pin power cable and will run off just the power supplied by the PCI-E port, while still running new games at good graphics settings.
My cousin wanted to play games like Mount & Blade: Warband and the latest games in the Total War series, (Napoleon: Total War and Total War: Shogun 2), at higher detail levels than he could with the hand-me-down Nvidia GeForce 7600GT 256MB that I bought back in 2006 and gave to him last year. He also wanted a new widescreen LCD monitor to replace the archaic 19" CRT he had been using. You can just tell that he's primarily a console gamer, can't you? I picked out an ASUS 21.5 inch widescreen LED-backlit LCD monitor with a low 2ms response time for him on Amazon, and an AMD Radeon HD 6670 to go with it.
I picked the Radeon 6670 because his budget was severely limited. I needed to find a reasonably fast gaming GPU that could be had for cheap and would run in his system without needing the additional expense of a brand new power supply. The 300 watt PSU in his Dell didn't have a 6pin power cable for higher-end GPUs, and couldn't provide enough power for one even if it had the cable. Having to buy a new monitor and a graphics card to drive it at the same time within a limited budget meant that buying even a lower cost 80+ power supply from a good brand like Seasonic wasn't an option in this case. So I went for a weaker card, which I thought would still be good enough for someone who isn't a framerate junkie or a complete graphics whore.
The Radeon 6670 is the successor to the 5670, which (I believe) was the second card in the Radeon x670 line, replacing the original 4670. These graphics cards all run fine in systems that have weaker power supply units, drawing power directly from the PCI-E port. They don't require upgrading to a PSU that has additional cables specifically for video cards like the better, more power hungry graphics cards do, but each still managed to provide reasonable gaming performance for its price point at the time of its release.
The 6670 is the newest, having been released to retail at the end of April of this year. The specific XFX model we got has 1 gig of 128-bit GDDR5 and came in at $75 after mail-in rebate, ~$99 without. I though that was a great deal for a card that lets my cousin play the latest Total War games at 1080p with most things set to high detail and at a decent framerate. It's no match for slightly more expensive cards that also require more power, like a Radeon 5770 or GeForce GTX460, but given that it's something so cheap that just sips power I was pretty impressed. Just make sure that if you buy this card you get the GDDR5 version, NOT the DDR3 version! The price difference is negligible but the performance difference is not.
I'd been waiting for the GDDR5 version of the Radeon 6670 to drop to a sub-$100 price point before I could recommend it, since it's not significantly faster than the old Geforce 9800GT I'm running in my gaming desktop, and for whatever psychological reason I couldn't justify recommending a card like that at above the hundred dollar mark. Now that the GDDR5 variants can be had for $99 or below, I think it's a great option for people who don't build their own computers to upgrade their mass market systems with.
There are other graphics cards that don't need higher watt PSUs with 6pin cables to run them, like a few variants of the Radeon 5750, but those seem to be a little difficult to find now. Most 5750 series and above cards require a 430 watt power supply with a 6pin cable as a minimum.
The scaling on the monitor was wrong with the default driver settings when I installed the card, the screen was set to the max resolution of the monitor (1920x1080) but there was a black border around the viewable area. Going into the Catalyst Controls and turning off underscan by moving the slider all the way to the right fixed this. I don't know why this happens by default, other people online seem to have had this issue too, but it's a quick fix.
I generally buy and promote Nvidia cards because I dual-boot Linux and the Nvidia Linux drivers have long been superior to the ATI/AMD Radeon drivers, but since my cousin uses Windows only and there doesn't seem to be a new Nvidia card with comparable price/performance/power traits, I went for the AMD option this time. It seems like the AMD Linux graphics drivers have improved at least somewhat since the last time I compared them with the Nvidia offerings, but they still don't seem to do VDPAU-style HD video offloading.
The XFX 6670 model that we got is a single slot card, is fairly quiet, and has HDMI, VGA, and DVI outputs. I've stress-tested and benchmarked it in my cousin's 300 watt Dell Inspiron 546 desktop and there were no problems. We can't max out Shogun 2 without dropping down to slow framerates, but we can set details to much higher than before and still get playable framerates out of it.
If you're looking for a gaming graphics card for a computer that has a weak PSU and you've got less than $100 to spend (and it's still close enough to the time I'm posting this that my advice is still relevant!) then I'd go for a Radeon 6670 model. Just make sure you pick up the GDDR5 kind!