I'm a student who lived in Rome last year - went and ate everywhere - and Rome is great for getting a quick slice of pizza, but the best by far is Lo Zozzone (or The Dirty One). For €3 you can have a huge slice of fresh white pizza, with whatever you want in it. Great quality and great price - I miss it so much.
Lo Zozzone, 32 Via del Teatro Pace,
(4 min walk form Piazza Navona)
Tel 06 68 80 85 75
Updates
I am from Rome and I used to go to the original Zozzone. I was very disappointed when I went again this year. I was treated really badly by the owner who could not be bothered to serve us our pizza. He got angry when we didn't understand that you are supposed to pay for the pizza first and get it after and we were ripped off when they didn't have one ingredient we wanted. We had to pay extra to substitute it with lettuce that was not fresh anyway. The pizzas without lettuce were decent, but no better than what you can get in any pizza al taglio, and a lot more expensive. Definitely not worth getting treated like an idiot and yelled at for.
Is this your business?