Does one need to make a reservation for any of the several airport shuttle services leaving Rome's international airport to the center?
It might be easier to just take the Leonardo Express train into Rome's central train station. You can get a cab to whereever from there. It's fast and runs every thirty minutes - just buy a ticket when you get there.
Terravision does have an airport bus that departs from Terminal 3 to Rome Termini. 4Euro. http://www.terravision.eu/rome_fiumicino.html
To answer your question. Reservations not needed.
Thank you.