The most common runaway I see has to be Hiawatha by some margin, though Alex, Nappy and Darius get honourable mentions.
On the other end of the scale, Cathy always LOOKS very impressive because her borders expand like nobody's business, but I find she always seems to crumble very quickly once someone DoWs her. However, I would say the least successful AI in my games seems to be Sejong - I think I've only ever had one game against him where he's survived as long as the Renaissance. He always seems to get squashed very quickly in an early war (to be fair, quite often by me)
Usually Siam and The Iroquois. Whenever I see them I know I have to eliminate them early, otherwise it'll be a massive war in the late game against a larger military
Hiawatha and to a lesser extent Pachacuti. Luckily Hiawatha is a good ally when getting rid of the other civs, as we both prepare for the inevitable showdown. So far I haven't really started next to him, not sure if he is equally friendly then.
My recent experience of that situation has demonstrated that he is most friendly except for those periods when he is actually at war with you, which is often enough.