We traveled to Rome in February 2005 and we did it all! I know some people think Rome is too touristy but there's a reason it attracts such crowds.
Rome was the center of the world for a time. The center of civilization, democracy, culture- everything. These days you have to look past the crowds and the street vendors and the gelato carts. You have to use your imagination to rebuild what was out of the ruins. But it's still there for you to discover. And the gelato is always a nice addition.