I'll be travelling to Rome for the first time in late November/early December. I'm middle-aged, but I've happily stayed in hostels in Europe. Is it possible to stay somewhere IN Rome for $25/night? Convents, etc. would be fine. Also, are there any events going on at this time in Rome that I should be aware of?

I haven't stayed at them, but from what I have read the Beehive and the Gulliver are both good hostels in Rome and would be in your price range if you are willing to accept a dorm bed.

http://www.the-beehive.com/home.html
http://www.bugeurope.com/reviews/Italy/Rome/

A great website to find out more about cheap stays (and hostels) is Eurotrip.com

Depends on time of year. In January 2003 I got a private room sans bath/wc for 30 euros. It was clean and seemingly safe and a few blocks from the train station, amidst dozens of budget hotels. It was nothing fancy and the room was tiny with no TV or view. For $25 you probably have to go the shared room hostel route even in winter unless staying several days, where you may be able to bargain down the rate.

The Beehive has private rooms with no bath for 30 Euros.