I myself I have never suffered any really serious intercontinental attacks from the AI. The worst I can think of was when the Persians turned up with some Galleons and unloaded a dozen-odd Inf and Cav next a poorly defended city (poorly as in defended by a single Cav unit). However, thanks to my railroads I could throw in a lot of troops, killing most of the invasion force in my turn, and seeing the pityful survivors commit suicide during their next turn by throwing themselves at my suddenly strengthened defenses. The Persians went on to have a thoroughly ****ed time during the Modern Age, since their huge Empire had just one source of Oil, which accidentally happened to be next to the city that was first in line for my invasion.
I've, however, seen quite substantial continentlets change hands from one AI to the next, which kind of implies that the AI is capable of more material invasions.