To start, why not visit the awe-inspiring Colosseum, a gargantuan structure which dates back to a time when Rome was the centre of the world, and slaves fought for their freedom within the vast, convex walls of this monument to power?
Try and plan a visit at night as well for great photos of this magnificent structure and Constantine's Arch lit up. If you are there for more than just great photos, a guide is recommended and is not always a rip-off - they can give an entertaining insight and lots of history on the place.
The ambient, English-style gardens of Villa Borghese are also home to a number of museums and galleries; here you can mix culture with the peace and tranquillity of the landscaped grounds. Bring a picnic in summertime and enjoy a lazy Roman afternoon.
The Fontana di Trevi, or Trevi Fountain, is the most photographed fountain in Rome; throw a coin in and legend says you will one day return to the city, but having seen Rome that's a given anyway. Certainly a beautiful sight, but a crazy place too; you may find you have to queue to take a photograph, but just take this in your stride and soak up the atmosphere while you wait.
Take a wander through the busy Italian neighbourhood of Trastevere with shopping, eating and drinking a-plenty. There's more of a small town feel here, where it seems you can escape the hordes of tourists and spend some time just watching the locals go about their daily business. Here you need not have an itinerary - just follow your feet around the many narrow streets and squares.
The Roman Forum is a free attraction containing the ruins of ancient roman civilization; it features the Arch of Septimus Severus, Temple of Saturn, Arch of Titus and the House of the Vestals. It's recommended to get an audio tour, which can be downloaded for free along with a map; or just join one of the walking tours for a reasonable cost if you are keen to really understand what you are seeing.
Planning a trip to Rome can seem daunting with all there is to see and do in a city of such historical wealth - Rome travel guides are your best bet, with information on hotels, attractions and car hire, it's best to get the advice of those of have already experienced at least some of what Italy's capital has to offer, and should therefore be able to point you in the right direction.