So Liz, you asked about Gocco. I'd never heard of it until I started wedding planning, so although I'm sure there are other uses besides wedding invitations, that's where I started.
Gocco is a desktop printing press manufactured in Japan, which works by pushing ink through a screen onto your printing surface. (Paper, cloth, ceramic - you name it.) There are a few different models of varying size, age, and sophistication. The screen is made by placing a black and white image against the screen surface, and using the Gocco housing to "flash" it with special bulbs. The heat from the flash melts the screen where it is exposed to the black image, which forms tiny holes through which the ink is pushed during printing.
The ink effect is very slightly inconsistent, which makes it look (in my opinion) both handmade and special. See above for perfectly imperfect printing.
There's a Flickr group for Gocco where you can see all kinds of gorgeous things, mostly paper.
There's a Yahoo group which is very informative for troubleshooting and locating supplies.
Elizabeth Anne Designs creates custom invitations.
And some of the Weddingbees have set the bar for DIY invitations.
Ok now, the bad news. Riso, Gocco's parent company, are no longer manufacturing the presses. They're still out there for sale, mainly used, but not in production currently. Worse, they are no longer manufacturing supplies. The big problem is bulbs; they're way too expensive to produce, so no one wants to take over the technology. There's been a lot of conversation on the Yahoo group about finding a substitute for the screen/bulb combo, but it's tricky. There are subs out there, but they're either super expensive (like tattoo transfer screens) or not as good for detail work. The most promising sub would be light exposure films, but where Riso screens have the capability of perforating only a portion of a mesh square, light and water exposures seem more inclined to dissolve all the media inside a mesh square. So although the mesh resolution should technically be the same, Riso screens are better than their listed 200 dpi. That makes the light/water screens less than ideal for, say, scripty wedding fonts where you could possibly get a pixellation effect where you wanted a smooth line.
So. If you're really into the idea, have some money to burn, and are willing to risk the supply shortage, buy a Gocco! It's loads of fun, and way more impressive than it is difficult. At least from an inking and printing standpoint. Plus, you could theoretically use it forever for all your wonderful personalized stationery needs. But if you just like the look, you can find artists on Etsy or talk to E. and A. at Elizabeth Anne Designs. Which is what I would do, if I weren't such a lousy little control freak all the time.