Why would you not want to visit this city? So many layers of history and culture exist side by side, never mind the incredible food.
The narrow streets are a web of interesting finds waiting to be discovered, whether incredible churches or divine ice-cream. The main tourist sites will be extremely busy, but it's worth wandering to feel the city. Yes it's worth seeing the main sights - you can't miss seeing the Colosseum and St Peters, however, there are many more interesting sights such as San Clemente with three layers of history or the incredible mosaics of Santa Maria Maggiore. Then again drinking coffee in a square or eat slices of pizza at lunchtime are much more enjoyable without hordes of tourists lurking around, even if it means that you are not directly opposite the pantheon, and honestly you'll probably get better food cheaper. Get a feeling for Rome without the tourists hordes and you'll fall in love with the place - its bustle, its beauty and its history.
Quick Tips:
Rome is not pleasant in the heat - in fact it's worth avoiding in the summer -there are plenty of more pleasant activities in Italy in summer than baking in the oven of Rome.
Plan the things you really must see - things you are interested in. Don't plan to see the 400 churches of Rome if you have no interested in church architecture, you'll end up just completely fed-up. For me most ruins end up looking the same after an hour - so Palatine Hill was simply torture! And unless you plan to spend eternity here you'll never see everything. But allow time to explore and not just sight-hop around the city.
Food can end up expensive if you don't use a little bit of thought. It has to be said cafes and restaurants close to main tourist site tend to be expensive and average. And just a few minutes away you'll get a better meal cheaper.
Best Way To Get Around:
Rome is probably best explored on foot to really experience the city beyond the usual tourist sights and to see the many gems you'd miss otherwise, never mind the atmosphere of narrow streets and squares. So get a good map and comfy shoes!
The public transport system is centred around Termini in the north of the city with trains arriving here (including the train from Fiumicino airport), metro and buses. The metro system is limited to two lines A (red) and B (blue) and is not all that useful for sightseeing unless you are staying near a station. There are stops close to the Colosseum and the Vatican which are useful. It should be avoid at rush hour as it becomes a sardine tin that is hot and unpleasant. Also note the doors show no mercy in closing so don't get in their way. They do have the advantage over the buses of not getting stuck in traffic, however the bus network crosses the entire city and is useful to get to many sights out of the centre like the catacombs.
The metro, bus and tram system has an integrated ticketing system with several different types of tickets available. The BIT is the basic type which is valid for 75 minutes after being validated and allows unlimited bus changes but only one metro ride per ticket. The BIG is a day ticket for 24 hours after being validated and allows unlimited journeys on buses and metro. There are also similar 3-day and 7-day tickets available. Be prepared to have your ticket checked by staff!