Traditionally, tipping in Roman restaurants has been limited to (at most) a coin or two for good service, or perhaps rounding the bill up to the nearest €5. This is standard behaviour, and restaurants are expected to pay their staff a decent wage; tipping just isn't part of the economy here.
Unfortunately, in recent years well-meaning visitors have begun to damage the system by leaving bigger tips; restaurants haven't been slow to spot this extra source of 'free money', and some places, especially those that target tourists, now levy a 10% service charge (servizio). (Often only to foreign guests; ask for the Italian menu and you'll see the charge has mysteriously vanished.) Some places are even trying the notorious double-dip, of expecting a tip and a service charge.
The best thing to do, assuming that servizio hasn't already been added, is to tip a euro or two at the end of the meal, or round up the bill very slightly. This may feel stingy and unnatural, but it's not: large tips may be usual at home, but here they're just a way of ripping off tourists. It even looks vulgar. Don't fall for it, and don't encourage bad behaviour by tipping big.
(In cafés, some Italians choose to leave 10c when standing at the bar, which is usually the change from a 90c espresso. If you sit down for your coffee, all the prices go up so you'll be paying through the nose anyway; there's no need to leave a tip on top of that.)