I am sure there are plenty of other offbeat guitar designs around, but you will find gathered here a few that are exceptional.
First we have the Manzer Pikasso I. You may have seen this around if you are a Pat Metheny fan, as it was custom made for him. It has four necks, and a ton of stings. The string tension on this puppy is around 1000 pounds (1000 pounds!!!).
Be sure to check the link for more pictures, and many other fine instruments (including the Manzer Pikasso II).
Next up is Phil Sylvester's site. There are many one-of-a-kind guitars and amps here, and they are all playable. Some of the designs are way out there, but still very cool. It looks like they are all for sale as well, and the prices don't look very reasonable.
There is a page for his guitars, and a page for his amps; I recommend taking the tour of each.
Finally, and probably my favorite (I am biased here, and I'll tell you why in a moment) Mike Doolin is a luthier who makes very fine guitars. This guitar was custom built for Justin King, and it sounds amazing–as do all the Doolin guitars I have heard, and I own one (hence the bias).
Though the Doolin guitar you see here is highly customized, standard instruments are available. This is what I own, and I could not be happier to own it.
Have fun drooling over all this linkage!