I'd say you'd need to put in two mid-end graphics cards and use the HDMI and DVI outputs on them so that you can drive two monitors from each (you can adapt the HDMI to DVI to effectively have 2xHDMI per card). 50 feet happens to be the spec maximum for HDMI, you can get longer runs by using a signal booster or, if you need a really long run, using a coaxial carrier system such as made by Gefen. These systems are very expensive though, so luckily I doubt you'll need one - a 100ft cable with built-in booster can be had for about $80 vs. $600 for the Gefen unit.
You could build a mini ATX system, the trouble is that you'll have a hard time finding a mini ATX board with 2x PCI-e x16, necessary for modern graphics cards. So, a more expensive but very practical option would be one graphics card capable of more than two displays. There's surprisingly few of these on the market. One route is a motherboard with SurroundView support, this allows you to use the motherboard's integrated video together with an ATI/AMD graphics card to get four outputs. The other route, and definitely the best one, is a video card that natively supports 3 displays. Matrox makes a lot of cards that will support up to 4 displays, but they're pretty expensive. Matrox is a real leader in the multi-display world (especially for signage and broadcasting applications), so definitely look through their catalog of video cards. This model, for example, looks absolutely fantastic but costs $500.
You could also look in to a TripleHead2Go unit, which would take three monitors and virtualizes them as one really big monitor so that your graphics card thinks it's only driving one. There are various finicky downsides to doing it this way, though, that might be an issue depending on what you're doing with the displays.
Edit: Two updates for 2012:
- Many graphics cards now on the market support 3 or even 4 or 5 displays on their own.
- A better choice for long HDMI runs now would be a system that runs HDMI over twisted-pair (cat5/cat6) cable, like those manufactured by Monoprice for only a couple of hundred.