Here's a necromancy.
Since I play exclusively on single player, I have no idea about the multiplayer dynamics and rankings of civilizations will be different for that purpose (but someone else should start the list for that).
So what I rank civilizations are based on their consistency, flexibility, and their power spikes (the earlier, the better, or usually around gunpowder when cannons come in). The rankings are based on the following settings:
-8 players (16 City States)
-standard map size Pangaea
-strategic balance
-no tech brokering
-no tech trading
-research agreements off
Disclaimer: I feel that EVERY civilization is VIABLE, however, there are a few that certainly stand out to be easier to obtain victory (or even stabilize) than the others. This is based on Emperor difficulty.
So here's my current civ ranking (version March 9, 2016):
S+: Korea
S: Babylon/Poland/Shoshone
S-: Maya/Morocco/Netherlands/Byzantium/America/Ethiopia/Persia/Iroquois
A+: India/Huns/China/Russia/Inca/Sweden/Rome/Ottomans
A: Portugal/Assyria/Zulu/France/Venice/Arabia/Austria/Inca/Celts
A-: Carthage/England/Indonesia/Mongolia/Siam/Denmark/Japan
B+: Aztec/Polynesia/Brazil
B: Greece/Songhai/Spain
B-: Germany/Egypt
And here are the brief explanations below. 
America
The ability to buy land from other civs is really strong. Especially those city states with Natural Wonders. The UU is pretty strong too, and the UB is good. And the early game sight is still a game changer.
Arabia
Strong UU (still one of the strongest in game, even after the horse archer ranger nerf), decent UB (it's nothing spectacular), and a good UA allowing him to get a "chain" of events. Solid civ.
Assyria
Strong aggro civ. Early game UU allows easy city captures and thus activating UA, and snowballs easily from there. The only problem is when there isn't a nearby neighbour trying to expand. The UB is just icing on the cake when you get writers.
Austria
Great UA, but a little dependent on other civs. But...with how often other civs conquer/spam Great Diplomats, you'd have to be willing to war them when you see one. Great UB, and a decent UU.
Aztec
Highly river dependent, but a good early game bully (though not as good as others). You'd have to be willing to wage war as soon as you see someone to abuse your UA and defend barb camps (so you can kill them yourself). The problem is just that the current authority tree isn't that good compared to the others, and Monte is highly encouraged to take it right away or he falls behind quickly.
Babylon
After the science changes, they're back to being top notch since the early academy helps a (insert expletive here) ton. It gets everything rolling, and if they have extra gold, their infrastructure skyrockets.
Brazil
With the Golden Age requirements to have their UA kick in, it's a massive liability early on, especially when their UU is so far late into the game to come into play. Surviving early game isn't easy with Brazil. Though the woodcamps help a little bit, it's not that helpful if you lack production. With that said though, they are pretty hard to control once they get to the later stages.
Byzantium
Warning: Incoming personal bias - I love this Byzantium. Early game cataphracts (20 combat stat this early?) at military theory, guaranteed religion (of YOUR CHOOSING!), combining the two makes it so dominant.
Carthage
Being able to invest into buildings immediately as you expand is a great boon. Early infrastructure really sets the pace for whatever you need the city to do later on. If you don't need to spend the gold on the city, then you're probably going to spend it on units anyway (or if you're feeling like gambling, invest into a wonder).
Celt
Lugh, Mannanan, and Bran are all pretty good pantheons. However, celts aren't always guaranteed a religion, and that's a pretty big bummer considering how good the pantheons are (probably meant to balance it out a little). Their UU allows them to get their pantheon early if you are able to hunt down a few barbs, and just hope from there that you are able to make it to a religion before they're all taken.
China
Strong UA. Strong UU. Strong UB. However, the UA's may be a little difficult to get going sometimes when the AI doesn't want to give you the luxuries early on. So it may take a bit to get the ball rolling, and that's probably the only strike I have against China.
Denmark
Good aggressive civ. Having earlier long swordsmen really go a long way, especially when they take no action points in pillaging. It makes the unit sturdier in an invasion, and most likely can take down any city other than capitals early on. Although, there may be an exception from cities with babylon's walls. But the UB encourages you to fight units anyway.
Netherlands
Extremely good UA since the wonders require culture to build now. Especially since each of them give 4 culture per turn. Polders are also extremely good. Although the UU isn't as great when I play pangaea, I would just consider it icing on the cake.
Egyptian
Great on lower difficulties. Otherwise is terrible since the UA regarding wonders is nothing compared to the AI, and is now culture locked anyway. So good luck even starting one when you have absolutely no bonuses for culture until artifacts (which you may get only a couple anyway since Egypt generally falls behind). The chariots are good, but that's their only saving grace.
England
Pangaea devalues the Ship of the Line by a lot and her naval bonuses are cut short as well. Although the extra spy is always nice. Her UB comes a little late, and usually is a little too late to recover (but if you got it while ahead, then you skyrocket, especially with coals).
Ethiopia
The Steele is still one of the absolute best early game buildings out there (if not the absolute best). The UA is also pretty good in jumping ahead on techs.
France
Nice cohesive UA. However, getting the slots for theming bonuses is pretty difficult. Their musketeers come at a very critical point and can be a game changer with the extra movement, and this allows the plundering to start. The only problem is getting a wonder to shove all that loot in. But overall, a great civ.
Germany
Getting alliances with city states isn’t easy as Germany on Emperor. Especially when the AIs get massive bonuses to compete against you. And with a UA that requires alliances with city states, it’s pretty much hoping the stars align for Germany to thrive. They have to wait until really late game for their UU to come through, and their UB is heavily reliant on other civs not sanctioning nor conquering other city states. Well…at least it’s better than Egypt.
Greece
Well, Greece is pretty solid at the moment due to the bonus combat stats of the hoplite, and possibly only because of that. Being able to get early generals and have early combat boosts matter (unless you face a Byzantium). However, unlike the Aztecs or Persia, they don’t have a way of automatically healing, and thus hurts them a lot.
Hun
Hun see. Hun take. Soon, Hun is going to be a big problem. Probably starting around spearmen or when they take a couple of barb camps.
Inca
The Inca is extremely good early game with their UI. Ignoring hill movement costs is a pretty big deal. It’s basically faster army, faster workers, and generally means a faster start.
India
Starting with a Pantheon will almost always guarantee a religion, especially if you pick the current “God of All Creation” where it’s basically guaranteeing you a religion. The UU is a little strange since it lowers the mobility of the skirmisher, but it gains plenty of durability (through feared enemy) and high stats. Although their siege is still suboptimal even though they don’t have that normal siege penalty. Better off using cannons. But their UB is also a bright spot for them.
Indonesia
UU is too random. UA is extremely good with an automatic monopoly (or a few). UB is decent.
Iroquois
Being able to move through half the map without hindering yourself (and on top of that, you getting bonuses from it) is extremely appealing. Being able to grab the early ruins even though you’re in the middle of a jungle is a good thing.
Japan
The UU is good. The UB is good. The UA requires a good dice roll to become relevant. Combat bonus is decent. Not bad by any means, but not really great either unless you have a great coastal start.
Korea
The nuts. Cannons upgraded from the Hwacha actually retains the two attacks promotion. The UA is insanely good (especially with reworked science), and the UB is good as well. Sure, you won’t be conquering anyone before cannons. But after the cannon… it’s doomsday.
Maya
The UI allows you to get an early tech lead and possibly secures a religion for you. It alone is outstanding enough to make Maya competitive, but with the ability to get a free Great Person every so often, it makes Pacal to be quite a force to be reckoned with. The UU isn’t that good though (but that’s beside the point).
Mongolia
Meet the neighbourhood bully that doesn’t need to hit you to hurt you. Just building up an army and going around annexing CSes is pretty satisfying. It’s not like you’ll lose any men either. The world will hate you, but you got an army to beat them down with anyhow. Good UB as well. The UU could be better, but having a free medic that buffs people around them isn’t something I would complain about.
Morocco
Just sending out caravans already makes Morocco strong with the bonus culture. The Kasbahs are also extremely good improvements. The UU is decent in regular terrain, but gets better in desert.
Ottoman
Getting the free volley upgrade is the highlight for this civ. The trade routes is also pretty good considering that the AI usually cleans the barbarians anyway. The Janissary is also a good UU currently, with the bonus of being available earlier.
Persia
The UA allowing movement bonus in a GA really pushes their siege units to being extremely powerful. Let’s not forget that immortals are pretty strong early on and can heal extremely quickly. This allows Persia to be extremely aggressive early, and can easily conquer other cities without much hassle. The UB is just icing on the cake for conquered cities.
Poland
I think this is the only civ that isn’t modified at all. And the funny thing is, it’s still one of the strongest civs. Especially since they recently got a buff (well, it’s more like a nerf for the majority of the civs) regarding the wonders requiring policies (guess who gets them for free?)
Polynesia
Great UU. Has half of the old Spanish UA. Pretty poor UI. It all depends on the dice roll for Kamehameha to be an actual force and not just a random early war guy.
Portugal
With the new science system, the UA is actually more relevant now and you can get a head start if you can get a trade route going early on with another CS. Later on, it gets better when you get naus. However, just like every other CS reliant civ, it’s a hassle to protect them, especially the farther ones.
Rome
Though Rome focuses on an early aggressive expansion stance, they can also switch over to conquer mode if necessary. The ability to retain buildings of conquered cities means that you should let them develop a little first before taking them over. So the Legion aren’t exactly the units with the best timing for that. But it’s probably best to establish a presence first anyway.
Russia
Catherine has a pretty useful UA in doubling all her strategic resources. This allows her to trade the excess away (usually for quite a bit of gold) and those same strategic resources give her bonus science as well. All in all, that’s the key selling point of Russia. The UB and UU are subpar compared to what others have, though the UU can actually fight infantry.
Shoshone
I think this is absolutely the most consistent civilization in the game. They will always be relevant. They have huge settling perks, extremely potent early game starts, and a great UI to boot. Unless you’re up against Washington, you’re going to annoy everyone else…but you can also wreck them too since you usually get ahead easily.
Siam
I personally dislike playing as Ramkhamhaeng, but his UU is extremely strong for the time frame it’s in. But again, the city states are annoying to defend, especially when everyone sends great diplomats from across the world to your allied city state.
Songhai
Askia depends on the length of the rivers you have in the city. The more river tiles you have, the better. The UU can be used mid-game to conquer cities more efficiently. But again, it all depends on the rivers.
Spain
Well, now that the Spanish gamble is gone, I do enjoy the more religious flavoured Isabella. Although she’s basically going to take someone’s religion and shove it into the world’s face, it usually comes at the cost of said person…and then the entire world hating on you. Overall, the UA and UB works well together. But the UU isn’t something that has an impact in Pangaea games.
Sweden
The new UA is very potent. Especially the extra movement on siege weapons. It’s kind of like Persia on steroids conqueror mode. Except that these guys start at gunpowder in general and they have a good UB to fall back on since it provides both science and culture now.
Venice
Venice, from being the joke of the base game, became actually viable. Hugely thanks to the Doge’s palace. That bonus start is crazy good, and allows Venice to actually be a big menace from the get go with the big head start. However, as with all diplomacy based civs, protecting the CS is a big problem. So he’ll usually just take them himself and start beating people up.
Zulu
Warmonger Shaka takes a little bit to ramp up, but when his units start getting multiple promotions, it’s basically trouble for everyone else. Impis are still an extreme terror, and with their double attacks (quadruple if you ever get to blitz with them, heaven forbid), things disappear really quickly.
