There is a lot of discussion about this in the forum, so I though I will clear this up once and for all.
* There is a fix rate (by law!) for FCO Airport-City (anywhere within the walls!): This is 40 Euros. All normal, official cabs (white!) cost this fixrate. To find these cabs, at the airport, once you get out of luggage claim and customs, go through the waiting area and go out of the building, where you will come across a street, with a long line of white cabs waiting. Go to the very right to find the starting point of the line, do not just get one from the middle of the line!
* Same rate applies to "from the city to the airport".
* For Ciampino airport this rate is 30 Euros
* All the other "transfer services", "limousines" etc. will cost more and don't have any advantage over the regular cab, so no need!