Feel free to disagree. This is all just my opinion.
Kazz's Civ V Tier List:
Pro Tier:
Catherine of Russia - "Strategic resources provide +1 production and Horse, Iron, and Uranium resources provide double quantity."
As though you weren't already grabbing all of those resources already. All those nice units that most people want to build as many as possible of? Well, you can have twice as many. Congratulations, you win. The Cossack is a fine unique, but the Krepost (replaces the Barracks) kicks fucking ass: it reduces the culture cost of buying new tiles by 50%. Meaning that her borders are going to fucking swell. She's unreal.
Alexander of Greece - "Your influence with City States degrades at half and recovers at double the normal rate."
City-States are a big deal this game. Staying friends with just one is an expensive proposition, so staying friends with several of them is almost out of the question for most Civs. Not for Alexander. He will have essentially double the little friends. And at a certain point, he can safely swap all of his cities to Production focus, since the food coming in from Maritime civs will be more than he could hope to make himself. Oh, and his unique units are straight upgrades of the Spearman and Horseman, giving him a better-than-decent chance of kicking your ass early.
Oda of Japan - "Units fight at full strength even when damaged."
How stupid-good is that. His ass-busted units are probably going to charge your city and push its shit in, no matter how hard you hit them first. It's such a cool and characteristic trait; I can completely imagine samurai on the attack despite having lost half their number and the rest of them being wounded. Anyway, Samurai aren't much stronger than Longswordmen but they do start with Shock I and make Great Generals spawn, which means you're almost always going to have a +25% to +45% combat bonus if you're at war in that era.
Ramesses II of Egypt - "+20% Production towards Wonder construction."
Hi, welcome to Civilization. Do you know how good Wonders are? They're good. They're extremely good. Any little boost toward getting them built helps, and +20% is not a little boost. At any rate, one fewer turn than the next guy is all you need to get a permanent boost to your civ. It will be very hard to compete with Egypt's wonder pile if he is not crushed early. Furthermore: the Burial Tomb gives both culture and happiness, making it kind of a mini-wonder that you can plop anywhere.
Wu Zetian of China - "Effectiveness and spawn rate of Great Generals increased."
Great People are cool and Great Generals are among the better ones, but I don't think this bonus is a huge deal. The best thing about China are its uniques, the Cho-No-Ku is an absolute rapist because it can fire TWICE IN ONE TURN, ARE YOU KIDDING, and the Paper Maker (which replaces the Library) gives the normal Library science bonus, but then gives you +4 gold too (+3 if you substract the Paper Maker's own maintenance cost). Most gold-boosting buildings give you a percentage increase, meaning that your city would have needed to already be a decent moneymaker, but the Paper Maker effectively gives you a free gold-producing tile.
Napoleon of France - "+2 culture per city before discovering Steam Power."
France tops a lot of other people's lists just because it makes cultural victory even easier. I'm unsure, really; +2 culture per city isn't a huge deal in my mind. But I can't really stick France in Mid Tier, either, because it gets such excellent gunpowder uniques, making it a mid-to-late-game force to be reckoned with. The Musketeer is 20 strength to the Musketman's 16, which is great, and the Foreign Legion (replacing Infantry) gets a +20% combat bonus OUTSIDE of your borders. A totally solid civ; France wins games, that's all there is to it.
Mid Tier:
Augustus Caesar of Rome - "+25% Production toward any building that exists in the Capital."
Why don't you just say "any building"? Cause if you're building it, Capital probably has it. Though you better hope (or make sure, if at all possible) your Capital is coastal or a lot of that bonus will be wasted. The Legion and the Ballista are decent uniques which thankfully share an era; too many civs have a unit in one era and a unit in the other.
George Washington of America - "+1 land unit sight. 25% discount when purchasing tiles."
The land unit sight bonus seems really good until you remember that, especially early on, there are always fucking trees in the way. The tile purchase discount is actually pretty good, I always find myself needing to buy a resource tile and saving a few bucks never hurts. America is best when it spams Minutemen, which have a nice movement bonus.
Askia of Songhai - "Receive triple gold from barbarian encampment and pillaging cities. Embarked units may defend themselves."
The gold bonus is far better than the bullshit bonuses given to Germany and Ottoman. Embarked units being able to defend themselves is also a big deal, as it makes a naval escort unnecessary (though still a good idea.) The Mandekalu Cavalry and the Mud Pyramid Mosque are both decent uniques.
Queen Elizabeth of England - "+2 naval unit movement."
The naval movement bonus is so good it's unfair, but it's so situational. You are basically forced to become a great naval power; what if you're on a pangaea, or the continents are enormous? You'd better hope the sea is really important. The Longbowman is a good unique, 3 range is a killer, and the Ship of the Line is easily the best naval unit for the cost.
Gandhi of India - "Unhappiness from number of cities is doubled, unhappiness from population is halved."
The normal unhappiness from number of cities is actually not that large, so this is more of a happiness bonus than anything, but with so many things giving you happiness if you need it, I'm not sure it's a good bonus. The best thing about India is easily the War Elephant. It replaces the anemic Chariot Archer, ranged strength 6 and combat strength 3. The Elephant has ranged strength 8 and combat strength 6, does not require horses, and doesn't have to stop if it enters woods or hills. It is a dominant early unit.
Harun al-Rashid of Arabia - "+1 gold from each Trade Route and Oil Resources provide double quantity."
Before I talk about the leader bonus, I should mention that the Bazaar provides an extra copy of each luxury resource near the city. Arabia is clearly intended to make money by trading with other civs, which is a cute idea, but do you really want to be giving away all those luxury resources and oil? I'd rather build a trillion tanks and keep the luxury junk to myself. A good civ to have as a patsy AI, a "meh" civ to play as. The Camel Archer (replacing the Knight), it should be noted, is an excellent unique.
Bismarck of the Germans - "Upon defeating a Barbarian unit inside an encampment, there is a 50% chance you earn 25 gold and they join your side."
What a stupid bonus. Historically, it makes sense, but good lord is this a chore. What you end up having to do, in my mind, is keeping a few nearby spots of land under fog of war, so that when late-game barbarians start spawning (Barbarian Riflemen, etc) you can go gamble on the chance to get free units. To keep itself out of shit-tier, Germany manages to have two good uniques: the Landsknecht is a Pikeman that costs as much as a Spearman (33 hammers), which is actually really cool, and the Panzer has 60 strength and 5 movement points to the Tank's 50 and 4.
Shit Tier:
Darius I of Persia - "Golden Ages last 50% longer. During a Golden Age, units gain +1 movement and +10% combat strength."
Eh. Persia is so close to being decent, but it doesn't work for me. The Golden Age bonus only gives you a bonus, yknow, during Golden Ages, so you'd better pop a lot of those. The Immortal doesn't strike me as a good Unique, just because it's a marginal improvement over an already marginal unit (the Spearman). Satrap's Court replaces the Bank and gives you a couple of Happiness, whoopee.
Montezuma I of the Aztec - "Gain Culture for the empire for each enemy unit killed."
Joke bonus. What strategy is that supposed to support, the cultural victory via constant warfare? Am I taking crazy pills? The Jaguar replaces the Warrior, yes, the very first unit. It heals 2 damage each time it kills a unit (how often will that be?) and it has a bonus fighting in Jungle only. The unique building Floating Gardens gives a bit of food, but is only even available if your City is built next to fresh water. Your strategy with this Civ, I imagine, should be to rush everybody at once and hope you can somehow kill every single other person on the map before they get ARCHERS.
Hiawatha of the Iroquoi - "Units move through Forest and Jungle in friendly territory as if it is Road. These tiles can be used to establish trade routes."
The Iroquoi's bonuses are ALL based on Forest and Jungle tiles. The Mohawk Warrior (replacing Swordsman) gets a combat bonus in the woods and the Longhouse (which you get after Metal Casting??? Go figure) gives a +1 production for each worked Forest tile. So you can't clear your forest tiles. So you can't automate your workers, cause they'll clear your forest tiles (I hope they give you decent automation options like in the old games soon). Also, don't misread that leader bonus: Forest and Jungle are roads in FRIENDLY territory, not neutral. Sorry to dash your hopes of using Horsemen like uber-Scouts or something.
Ramkhamhaeng of Siam - "Food and Culture from friendly City-States increased by 50%."
Many of the civs in the Shit-Tier list shoehorn you into a strategy without giving you the tools to make them work. Alexander's City-State bonus is great because it actually makes it easier to have a lot of City-States on your side. Ramkhamhaeng's City-State bonus sucks because, while it gives you a substantial boost to the support that they give you, they are going to remain just as expensive to make nice with. City-States are powerful allies in number, but having just as many as the next guy doesn't constitute an "advantage." Siam's uniques aren't great; Naresuan's Elephant is slower than the Knight and has a bonus against Mounted, and the Wat is a University that gives 3 whole entire culture.
Suleiman of the Ottomans - "50% chance of converting a Barbarian naval unit to your side and earning 25 gold."
This bonus is dumbfounding. You have to understand that the Ottomans DOMINATED much of eastern Europe and the Mediterranean in the middle of the previous millenium. This bonus fails completely to reflect that. I don't even get how you're supposed to use it. Like, go back and read Russia's or Japan's, and then come back and read this one. Whatever; the Janissary (replacing Musketman) is actually a pretty dangerous motherfucker because it fully heals if it destroys an enemy unit (though I'd rather have Japan's bonus than a billion Janissaries). The Sipahi replaces the Lancer; he gets +1 sight and it can pillage for free. What fucking garbage.