Reading around the 'net, and here, has lead me to believe that SFF computers need to mount to the back of the monitor to really be out of the way. This also reduces cable clutter, giving an almost black-iMac-like look.

Does anyone know of a VESA-mount case that can hold a single full-sized graphics card?

No quite, but I've seen two that allow a full size graphics card and double as a monitor stand.
Chieftec BL-01B. Here's a review by overclockersclub.
I can't find the second one at the moment. It was a very wide case to put behind the monitor, maybe even with a vesa bracket, if it actually went on sale i don't know. I will post back if I can find it.

Hah, found it:
Jersey G60
200€
if there's a case I haven't seen it's probably only available in Japan.

Wow! This case looks amazing. I remember looking at the reviews when it came out. I dismissed the case because some of the reviews said that the case metal was thin. Thin cases never stop noise, and the sides can turn any vibrations into loud noises.

It appears that this case was discontinued a few months ago after three years of poor sales. I'm going to pick one up after the next paycheck and move my Linux system into the case. I expect that I can attach a 27" LCD if I am willing to give up on rotating it by 90 degrees.

It is crazy that they did not put a handle at the top, as this would be the BEST LAN Party case!




Please find any other case like this. It is good if everything is internal. External power supplies and length-limited video card slots are the stupid trends in desktop computers. Once you have committed to a desktop form factor, it makes sense to make everything internal and high-powered.

To revive an old thread:
Gigabyte GB-AEGT barebone 24" full HD screen, socket 1155 with room for a dual slot graphic card.

That Gigabyte barebone computer looks good, but it would need to be at or under $500. I also expect that it will limit the power of the video card to "mainstream" cards that use under 200 watts. If anyone sees a review, please link to it from this thread.