Special models
There have been many manufacturers who wanted to give their guitars something extra.
Sometimes with a clear and distinct funtion, sometimes only to give the guitar a special look or shape.
Jimmy Page's double necked guitar had a very distinct function because of the combination of a 6- and 12-string guitar.
The design of a headless guitar has a clear function too, as also the silent guitars and the harpguitar.
The guitars of, for example, B.C. Rich have mainly a different shape to create an own recognizable face. Often function is made secondary to shape.
Nota bene: my own Maverick X1 has this flaw too. A traditional shaped guitar really has a better balance.
More pictures of specials? Watch:
http://www.xigre.com/articles/music/Weirdest_guitars_in_the_world.html