A few years ago an agreement was signed on fixed tariffs from Fiumicino to the center (defined as any location within the Aurelian walls). The agreement is exemplary simple and transparent: the trip costs 48.00 euros for up to 4 people including luggage, no matter what day of the week and what time of day we are talking about. NB. This agreement applies only taxis from the Municipality of Rome. They are white and have a sign in A4 format on the front doors, where the tariff is clearly indicated. The sign also reports the taxi number so that customers have easy access to recognize if the driver were to require more than the tariff. Taxis from Fiumicino Municipality do not take part in this agreement: your fixed tariff for the trip to the center is 60.00 euros !. Private drivers in neat suits with their big, well-maintained cars that are often trying to poach customers outside the arrivals hall, on the other hand no bargaining about the price. They work for one of the many private agencies that offer transfer (and everyone else runs), and they will often be called upon if there are more than can fit in a regular taxi. We will not highlight one company over the other, but you can easily find them by searching on the Internet, and their prices are quite reasonable (when you just make sure to order them in advance). If you land at Ciampino applies to all of the above, the price of the trip is just only 30.00 euros.
For many years, most tourists take the direct train from Fiumicino to the main train station Stazione Termini, the so-called "Leonardo Express". It still exists, and the trip will cost 14.00 euro pro persona (or 16.00 euros if you do not buy the ticket in ticket sales, but in one of the kiosks). The trip takes about 30-35 minutes. Today, this option does not make much sense, since the buses cost less and only take a little longer.
You can also choose to take the regular train, but not running to Stazione Termini, but to Stazione Ostiense, from where you can take the bus or tram to the center. This option costs 7.50 euros for the train ride and 1.50 euros for a bus / tram ticket. It is especially recommended if you need to go to Trastevere, so you can get off at Stazione Trastevere and take tram line 8 on. It is also a good solution if you need to stay near Campo de 'Fiori, then you just stay a little longer on the tram and get off at "Arenula / Ministero di Grazia & Giustizia" or the next stop at Largo Argentina.
From Ciampino airport you can take the bus to the train station in Ciampino town for 1.20 euro pro persona and there take the train to Stazione Termini for 1.50 euros.
Over the last years, several bus companies began to compete in the transport of people to and from the airport. It has largely a benefit to our consumers as prices have gone lower and lower. Currently (June 2015) a ticket from Fiumicino to Stazione Termini or the Vatican costs you only 4-6 euro.
When you depart the arrival hall, you walk a few hundred meters to the left and you will find shuttle buses. Before you get that far you will pass the bus company ticket booths. But there is no reason to buy the ticket before you get to the taxi rank, the price is the same and you can very easily see who is running first, once you are out there. The same applies to the possibility to book tickets over the companies' websites: Only the maximum could save 1 euro pro persona (often the price is the same), and you will lose flexibility. The journey to Stazione Termini takes about 40-50 minutes, depending on traffic intensity and the driver's mood.
At the time of this writing, the company Terravision runs directly lines between Fiumicino and Stazione Termini, while the company SIT addition Stazione Termini also runs from / to Via Crescenzio by the Vatican, the company T.A.M. runs from Stazione Termini the Stazione Ostiense, and finally also runs Schiaffini Travel directly from / to Stazione Termini.
From Ciampino, the story is the same, only here are only two companies to compete for customers. Prices are roughly the same as for Fiumicino.