I find most civs are hit-or-miss, but here's my list of standouts in one direction or another.
First up in the "Oh no, not you again" category:
SHAKA of the ZULUS
HIAWATHA of the IROQUOIS
SEJONG of KOREA
ALEXANDER of GREECE
We know why Shaka's there. The Zulus are dangerous in anyone's hands; throw an AI's bonus happiness and gold in and they're a menace. Program that AI to expand like crazy and kill everything in the way, and now they're a very dangerous nuisance the AI can do quite well.
Hiawatha's a different flavor of pain in the ass. Use that happiness to fund countless little craphole towns all over your territory, and make him quite testy about you being on his sacred native land and now he's an annoyance. He's also seemingly got a taste for science.
Sejong... we all know what he's capable of. If he's on another continent unmolested, start planning your late-game assault now. Right after you find him he's probably got a fleet of Hwa'cha and Turtle Ships, so you'll have to push after he's strongest and hope he didn't run away too far.
Alex we know all too well. I'd put Siam here too for similar reasons, but Alex is better at gobbling up city states, while Siam just enjoys the benefits more. Alex is a little more willing to try to kill you too, despite Rammy loving Stampy the Elephant spam.
Moving on to the "Total non-factor" category:
ASKIA of SONGHAI
PEDRO of BRAZIL
ENRICO DANDOLO of VENICE
?????? of MOROCCO (I can't even be bothered to remember his name)
Askia I really don't understand. I just finished a game as him and I have to say that the Mud Pyramid Mosque is quite nice and the extra gold early-game is quite useful. My running theory is a combination of mixed-bag priorities for the AI, and that the AI is quite used to pissing away extra gold, so triple from encampments can be wasted easily. I've seen this guy fail in so many ways; from doing nothing but building Warriors on one city, to just sitting by idly waiting to die.
Pedro. Poor Pedro. My running theory on why Pedro dies is that he's quite passive, has a jungle start without a human's knowledge on how to work one of those, and his uniques only matter very late in the game if ever. Extra tourism in a golden age means you need to get a lot of them, and Pracinhas are the single latest UU in the game, with marginal utility even then. The Brazilwood camp is nice but won't save him.
Enrico's failures are due to the fact that Venice is so strange and unique that it'd require a second set of AI to play him, I think. I know the AI doesn't understand this guy because he gets upset when I settle nearby. Dude, you were never putting a city there and I know it, now let me trade you the gold you'd never be able to work.
Morocco: one of the worst UA in the game that desperately needs some scaling. Kasbahs really need good desert to work well in. Berber Cavalry are neat, but only good on the home game, and this AI is too passive to work it.
Finally onto the "dice-rollers" category for either very good or very bad results:
GHENGIS KHAN of the MONGOLS
ISABELLA of SPAIN
CATHERINE of RUSSIA
WU ZUTEIN of CHINA
Ghengis depends entirely on how his city-state devouring pays off, and how his time period with Keshiks goes. Either he's a really big powerhouse, or he's had the crap kicked out of him for messing with city-states. More the latter in my experience, but I've had some close calls.
Isabella depends on how many if any free settlers she gets, and then how well they get placed.
Catherine I've seen do really well with expansionism, but every once in a while she steps on a toe too many and gets her butt kicked.
Wu I've seen play the passive science game one too many times. She's no Korea or Babylon. Sometimes it works (she's running away in my current game as Germany), but sometimes it doesn't.