See here: http://www.operaroma.it/.
The one opera to see in Rome is Tosca by Puccini; on opening night. This is the tradition because Puccini first performed this opera in Rome at the same opera house (they still set up the original set from the first one held there in 1900 - 110 years ago!).
By divine providence yours truly was able to go on my birthday in 2004 and in the old Savoia royal box sat the distinguished president of Italy, Signor Ciampi.