There's a whole section on these boards dedicated to oil.
Oil and Lubrication - Ducati.ms - The Ultimate Ducati Forum
The quick and dirty answer is that I run Rotella T6 fully synthetic on the street. It's 5W40. I change it every 2000 miles. My drain plug magnet and oil screen are always as clean as can be. I also have never seen an oil temp above 240 F, and that's with a medium aggressive riding style in a hot Southeastern climate.
If I were going to put it on the track and saw higher temps I'd probably run an xW50 synthetic and do an oil change immediately afterward. The real key is to have enough viscosity to supply adequate oil pressure at whatever temp the oil runs.
That's my opinion though. You'll have as many opinions expressed as you get responses. The following website can give you some info concerning oil in general and they also have a useful forum.
- Bob is the Oil Guy
Have fun on your track day.