Question: Are there any extruders and printers that do a good job with ceramic clay?

I assume the clay has to be fine grained and with enough water added to be able to be pushed out through the extruder's nozzle. I also assume the print speed would have to be arther low for the already printed layers to gain stability before printing the next layer. Perhaps some extra equipment on the printer to spped up this drying process?

At the same time, the print speed can't be too low: if the bottom starts to dry enough to start shrinking, the object will crack.

Also, some solutions I've seen tend to result in rather low resolution/thick layers, which is negative.

So, what equipment is "out there"?

Answer: 
What you are looking for is the Frostruder style extruders.

Here is a link to a [thingiverse file for it](http://www.thingiverse.com/thing:1143).

You honestly cannot expect fantastic results but it will get the job done! There are many other types. Quality will depend on the size of the point. However with something as high viscosity as clay I would not expect you to be able to push the quality very high.
I cant speak for the quality or type of clay, but there are several designs out there that print in clay. Here is the first one that popped up on my google search.

<http://www.wasproject.it/w/en/wasp-launches-the-new-professional-clay-extruder/>