I haven't been to Rome in a long while (a dozen years maybe), but would broadly echo Hamm and clivex's recommendations.
Photos by the Trevi Fountain are a must-do; if only to tick one off the movie-scene list, and to marvel at how hideously hemmed-in it is (unless, in the intervening years, they bull-dozed the litany of ice-cream parlours, tatt/gift-shops and snouterias that used to border it).
A wash of the hands in the fountain at the foot of the Spanish Steps will reputedly bring you good-luck (though apparently only if you're fu*cking Spanish, if my experience is anything to go by) and Byron's gaff is close by too.
I agree somewhat with the comments about the Vatican Museum....unless you're a huge fan of tapestries and frescos, in which case it should be on your list. There are undoubtedly some greats works on display, but it has a rather dry - dare I say even chintzy feel - and even the Sistine Chapel managed to underwhelm me to a degree. The Louvre would knock it into a cocked-hat, by way of comparison.
St Peters is stunning yet somehow left me feeling cold too.....as if I'd inconsciously moved a step closer to the Reaper. Maybe that's the intention? Either way, the chapel (it is a chapel, right?) is probably worth a view. And you can wander down through the Square to Castel SanAngelo, and take a walk down the river until you get to the back-side of the Forum.
Stop me if this starts sounding like a Dan Brown novel.
Anyway, it's a nice walk (and a nice route to reach the Forum/Colloseum).
