We purchased a Roma Pass at the airport upon our arrival in Rome. We had researched the pass before the trip and we knew we would make good use of it.
The pass entitles you to free admission to 2 museums/monuments, discounted admission to other museums/monuments, and 3 days worth of travel on public transit (trains and busses).
We used our pass to enter the Colosseum and Forum (one museum/monument combined) and the Castel Sant'Angelo. We also used it many times on the Metro. Our pass more than paid for itself and it was easy to use.
The children did not require passes and when we went into the monuments we were issued free tickets for them.
The only downside of this pass was that we could not figure out how to use it at the Borghese Gallery and because of this we could not go to the gallery because all of the tickets were reserved on the day that we were there.