Before traveling I read that Rome is best done quickly, so I planned for one full day—plus the next morning. After a missed flight we arrived late, which cut our time down to one afternoon and one morning—much too little. Plan a full day for the ancient sites: Colosseum, Forum, Palatine Hill, Pantheon; then do Trevi Fountain and Spanish Steps at nighttime, when they are at their best and everything else is closed anyway.
A few notes on the ancient sites:
Buy your Colosseum tickets at Palatine Hill (no lines, and tickets sold at both locations automatically include entrance to both sites). If you spend too much time at Paltine Hill, your Colosseum ticket is good until 1:30pm the next day (but be careful if you're planning to visit Vatican in the morning, you'll never make it back in time).
Don't leave sight-seeing too late... the Pantheon closes at 7:30pm Mon-Sat and 6pm on Sundays.
You'll want to dedicate a good portion of the next day in Vatican City. Keep in mind that the Vatican Museum closes early, so do this first.
Another hint about the museum:
The lines to get in can be horrendous. I suggest reserving a space in the tour group fax 06-6988-4947. After a Vatican City gelato go to St. Peter's or take the "Group only" exit at the back of the Sistine chapel to go straight to the basilica and skip the line.
Quick Tips:
Best Way To Get Around:
The major sites in Roma aren't too far, and you can do most of your sight-seeing by foot. The train station, most hotels and the ancient sites can all be done by foot (with a sturdy walking shoe). You will want to take the Metro line A to get across the Tiber River and over to Vatican City.