If a civ has a * next to it, that civ is on a higher tier when dealing with Pangaea and other land-heavy maps.
If a civ has a ^ next to it, that civ is on a higher tier when dealing with Archipelago and other water-heavy maps
Basically:
God Tier = Will almost always win. These civs have such powerful advantages, it's insane.
High Tier = Great civs, might be worse in certain situations, but are in general almost always good picks.
Upper Mid Tier = Good civs that might be either overspecialized or too unfocussed, or need certain starts to work.
Lower Mid Tier = Decent civs that have a few downsides to prevent them from being truly good, but if the dice roll works out, they can do very well.
Low Tier = Civs that aren't trash, but don't offer enough to justify picking them over pretty much any other civ, really.
Bottom Tier = The worst. Sure, they can win the game, but whatever job they want to do, another civ is almost always better at it.
Gamble Tier = Spain
God Tier:
Babylon
Korea
Poland
The Maya
These are the only four who will always, no matter the maptype, dominate the game. Three of the four have science bonuses, which are huge, though the stronger the scientific bonus, the lower the flexibility. Poland gets a free oracle each era. That says enough.
High Tier:
Arabia *
England ^
Ethiopia
Celts
China
Egypt
Inca
Shoshone
From here on, let's go by them one by one. Arabia is a dominating force and will have a lot of gold, but on watery maps they'll find their Camel Archers less powerful, and their UA becomes worse. England is great in Deity for spy-tech-catchup. They hold themselves well on land with 2-range-gatlings in the late game, and on the sea they obviously rule. Ethiopia and the Celts are both here for flexibility granted by near-guaranteed religion. China has a stronger early game, has a powerful UU and in general is among the best of the warmongers. Egypt is flexible due to free happiness building - a rare commodity - and they can attempt wonders other civs won't dream about. The Inca are near-god-tier due to their massive cities in locations others won't dream of building, combined with army flexibility. The Shoshone have the best early game of all civs, leading to snowballing advantages.
Upper Mid Tier:
Mongolia *
Rome
Siam
Venice
Morocco *
Aztecs
Persia
Mongolia does one thing good but it does it SO good, they're pretty high up, but they falter on water maps. Rome is flexible and can get sattelite cities up to snuff easily. Siam's huge benefits from CS's helps them go various directions depending on what they find. Venice will have all the gold to do whatever it wants, but is on the vulnerable side. Morocco is defensive, rich, but not very exciting. The Aztecs can have gargantuan cities even without lakes, and will be able to get quick culture through barbarian farming. Finally Persia is the definition of a boring but effective civ. They're not bad at anything. At all.
Lower Mid Tier:
Netherlands
Portugal
Zulu *
Greece
Sweden
Austria
Assyria *
Huns *
Russia
Netherlands are the best at early wealth, but they do need specific terrain for their other strengths to come into play, however they can settle inhospitable marshlands. Portugal is rich, but not nearly as much as Venice and also doesn't have any other true strengths. The Zulu are a warmonger through and through, but the Impi isnt as effective as a Keshik. Hence Mongolia > Them. Greece's gold saving through not spending it on CS isn't as big as you'd think and their UU's are useless. Sweden requires a specific gameplan and has an annoying starting bias, but they can be oh so explosive. Austria is hampered by needing a few turns before CS annexation and a poor UU, but their UB does help, keeping them decent. Assyria wants to be an early warmonger, just like the huns, and they're certainly good at what they do, but early warmongering is frowned upon especially in the lategame. Russia is all about exploiting that extra production and some gold from trading away early iron/horses, as well having larger borders, but they aren't as flexible as top-tier civs.
Low Tier
France
Polynesia ^^^^^^
America
Brazil
Carthage
Germany
Indonesia ^
Japan ^
Songhai
France may have a decent culture game, but it comes into play late, leaving them vulnerable. Chateaus dont seem to yield enough either. Polynesia is ONLY good on very heavy water based maps, otherwise they're kinda crappy. America is the definition of a vanilla civ, but they have a few useful tricks at least. Brazil has a very slow start to the point of being tedious, but they can blow you out with sudden huge tourism. Carthage has early game gold, larger trade routes...and once other civs reach navigation they're bad again. Germany's Hanse is their saving grace, but you can't trade with other civs if you want to abuse it, nor run the usual better internal trade routes. Indonesia's Candi is a good building and if you can settle some other lands you're in good shape, but they're too map-reliant. Japan wants a coastal start with Iron to do anything, but if you do have some sea resources, it's smooth sailing. Songhai, finally, has good bonuses at it's core - they're just not strong enough each on their own.
Bottom Tier
Denmark
Iroquis
Byzantium
India
Ottomans ^
Denmark is great...at a gameplan that BNW doesn't appreciate. Ski Infantry is in contention for worst UU, too. The Iroquis have the distinction of having the only UB that's worse then the building it replaces, along with a meh UU and an UA that is too restricted. Byzantium would've been great if they just had any form of faith-producing bonus...ANYWHERE. Dromons are nice for sniping though. India was once the definite bottom of the barrel, but with one HIGHLY specific playstyle, you can grow some massive cities...and that's it. The Ottomans finally are build to be pure warmongers, but Privateers already have their UA (And earlier ships don't do much warmongering anyway), and their UU's, while decent, won't carry them the entire game.
Gamble Tier:
Spain
Find Uluru, Siri Pada, Great Barrier Reaf, Lake Victoria, Mt. Kailash, Mt. Fuji, El Dorado, King Solomon's Mines or Fountain of Youth in settleable distance? You're God Tier. If not? Well, Conquistadors are still a decent unit and a way to still get those wonders.