Quite a lot has been written about this subject over the years, especially regarding the removal of the breather to be replaced with a mini 'K&N' style filter.
This is generally considered a bad idea and detailed here:
http://www.ducati-upnorth.com/tech/breather.php
As Nick says, the original set up is driven by emission regulations but the canister behind the vertical cylinder actually houses a one way valve to prevent anything returning into the crankcase, leaving any vapour to either become liquid in the black plastic catch tank mounted on the frame or to be recycled hot oily air taken in via the air box thus meeting any emission regulation originally set out during those production years.
However, the system can easily be made a little better without affecting the crankcase pressure by removing the pipe that returns the hot oily air from the breather catch tank to the air box (ideally you'll need a little extra pipe to vent the box away to the free world).
This set up will then let your motor only take in nice cool, fresh and clean air from the outside world through whatever air filter you're running.