Colosseum, Forum, and Palatine Hill (all combined under one ticket)
The Roma Pass is a combo ticket good for sights (including the Colosseum/Forum area and Borghese Gallery), in addition to a 2 or 3-day public transit pass.
In Rome Now has the latest for concerts, exhibitions and more.
ATAC has route planning information for the local public transit service.
Trenitalia is the national train operator for journeys near and far.
Italo is a private high-speed train service connecting the major Italian cities.
Seeing the Pope:
Santa Susanna, home of the American Catholic Church in Rome, is a wealth of info (including Papal Audience tickets).
The offical Papal Calendar.
Weatherbase lists the year round average temperatures.