Rome was not built in a day, and it cannot be seen in a day. Italians say that the lifetime is not enough. In reality, a week is enough to decently scratch a surface of the Eternal City, and even in a day you can get a taster that will bring you back for more.
Rome has everything from great shopping to great art, food to architecture, antiquity to modernity.
How to make the best of what is such a little time in which to fit so much? The answer is, don't try to do it all - don't even try to fit the major sights in. Start early, get comfortable shoes, a good map and don't be afraid to use public transport. For a typical visitor, interested in historical sights and noticeable landmarks, this is a suggested day's itinerary
Start at the Vatican. Visit St Peter's Basilica, the Mother Church of Catholicism and arguably, the greatest Christian temple in the world. Don't miss the Michelangelo's Pieta, Bernini's Baladacchino (it's probably impossible to miss this Baroque orgy of twisted columns and gold ornamentation) and, unless you are scared of heights, do climb to the top of the dome for wonderful vistas of the whole of Rome in general and the Piazza San Pietro below in particular.
Unless you are very keen on paintings and came to Rome especially to see old masters' art, DON'T go to the Vatican Museums. Even a very perfunctory visit requires hours and will leave you exhausted.
Take the metro to Flamino to have a look and throw a coin into the famous Trevi Fountain and a walk round Piazza del Popolo. Have a coffee or a snack round here and then take a bus no 117 or 119 all the way down Via Corso to Piazza Venezia, dominated by the huge monument of Vittorio Emanuelle. Bear left to Via del Teatro di Marcello and climb the Concordata steps to Michelangelo's masterpiece of High Renaissance, Piazza del Campidoglio. Visit the Capitoline Museums for some excellent sculpture and some great paintings, including Caravaggio.
Walk down the steps to the left side of Palazzo Senatorio, they will take you down to the Roman Forum. Explore the ruins of temples and basilicas of the Forum, walking the length of Via Sacra from the triumphal arch of Septimius Severus to the arch of Constantine (itself outside the Forum area). Now you are at the Colosseum and it's probably some time in the mid-afternoon. Visit the Colosseum briefly if you feel up to it.
Take a bus no 87 or 186 from near the Colosseo metro station to Corso del Rinascimento (ask for the best stop for Piazza Navona). Explore the fountains and buildings on Piazza Navona, there are plenty of cafes for a pit-stop round here. Pantheon is only a stone's throw east of the Piazza, so it's worth a look if you can make it.
Have a dinner here, or head south towards Piazza Capo di' Fiori. If you are still capable of walking, conclude the day with an evening walk along the Tiber.
And then, start planning your next visit.