The most unloved Ducati beveldrive twin, and probably the only one that, if built into a cafe racer, would not draw the scorn of purists:

http://cgi.ebay.com/ebaymotors/1977-Ducati-860-Bevel-/180651292727?pt=US_motorcycles&hash=item2a0fa7f837#v4-42

Be sure to follow the video link halfway down in the seller's description. Listen to how nicely it starts and runs.

With clip-ons, a bum stop seat, and relaced rims, you would be a bike show contender at a RvM or AHRMA event.

Add mag wheels, an overbore kit, some big carbs, upswept megaphones, a bikini fairing, and ditch the starter and the metal fenders, and it could look and sound as cool (and start as poorly) as this:

John Britten Ducati 860

Cool idea.  But it is a bit... plain currently.  Needs some stickers 

It sold for $5200... At that price, I wouldn't have been able to afford any stickers! Man, even the ugly Duc-klings are selling at a premium.