So what happened to the Supersport?

[ducatiz]

Plus, with the pre-'98 models, you can run across such potential issues as

cracked frames,

affected about 5% of bikes made between 94 and 96.  ducati replaced the frames for free (you had to pay labor) even after warranty.  the crack was at the yoke and is repairable by gusseting the yoke.

cracked swingarms,

this was only on the aluminum swingarms and was due to over-torquing the swingarm pin pinch bolts.  Ducati revised the torque and that was that.

pulled/stripped head cylinder studs,

broken studs!  very nasty. relatively cheap to buy but expensive to replace.  any engine rebuild on the older 900ss should replace the stock bolts.

and a couple of other things that I cannot remember right now.

galley plugs not being staked properly (affects almost all 900 engines) and result in zero oil pressure if it backs out (you'll get metal in your oil first for about 10000 miles), crappy carb setup with super-long manifolds.

Honestly, I feel most of these problems represent the "old" Ducati mentality of building things.  90% of them disappeared when Ducati was bought by TPG.

i know of plenty of 900ss models (92-97) with zero problems and it's rare for these to cluster on one bike.  my 900ss had the galley plugs back out a bit, so I got the engine rebuilt and the plugs staked properly.  in the process i replaced all the bearings, put in high comp pistons, new studs, got the heads ported and flowed, short-manifold FCR carbs, got the frame gusseted, and a few other things. 

damn thing wheelies in second gear and i still get about 40 mpg..

[RichD]

...I've heard that the pre-'99 models are ...not as well handling. Plus, with the pre-'98 models, you can run across ...potential issues as ...pulled/stripped head cylinder studs, and a couple of other things...

The handling change is due to a different length shock ('99+ are about 3/8" longer) -a simple change.
The head studs would crack but the threads are fine.
The aluminum swingarms could crack (not that frequently) -the steel ones had no problem.
The frames were more likely to crack than the swingarm (but very fixable if you TIG).
The aluminum oil passage plug in the crank could back out.
Single phase charging systems don't like neglect, and the regulators (when failed) would boil the battery dry.

...but my '97 SS is hands down my favorite bike.
If I had to keep just one, that would be it.