Here's my reposted list, now with reasons. I also moved some Civs, and I'll probably move them later again. Please respect this is only my personal opinion based on my personal preferences and experiences.
Part 1:
24, Norway (Harald Hardrada)
Norway is, without a doubt, great naval civ. Both UA are offering naval bonuses. But navy in this civ has one big problem - it's nearly useless. You need only 3-5 ships to sink enemy units and wreck their coastal cities. Stave Church is slightly upgraded Temple and doesn't offer nearly any bonuses. Viking Longship is better Galley, but, as I said, it's useless, because it becomes obsolete soon and because it's close combat ship. Berserker is quite strong, but one good UU can't save horrible Civ from being horrible. Firaxis, if you'll make another naval Civ, like Dutch Empire or Venetian Republic, make it stronger. Please. Or at least improve naval warfare of the AI.
23, Spain (Philip II)
Insignificant, that's what can I say about Spain. Treasure Fleets offer small trade route bonus, that's okay, and allow me to combine ships into fleets and armadas sooner, which is nice, but still doesn't change the fact that navy is almost useless. El Escorial is the same. It offers me battle bonus agains enemy with another religion, which is good, and allows Inquisitors to remove heresy three times, which is fine only if you have annoying religious neighbor and if you're going for Religious Victory. Mission is insignificant UI. Conquistador can be decent UU if you have religion and enough faith to buy enough Missionarries and Apostles to increase their power.
22, Rome (Trajan)
I'm sorry, but I really don't like this one. All Roads Lead to Rome is one of the worst abilities in the game. Many people like Trajan's Columns, but I don't. It's maybe good for early expansion, but I almost never early expand, so when I settle, I usually earn enough money through foreign trade routes and Commercial Hubs to buy a Monument, so this is only "money saver" to me. Baths are great district, because extra housing and amenities are always welcomed. Legion is good UU, with slightly higher strenght and no need for Iron. Its ability to build Roman Fort is useless for me. But good UU and UD doesn't save Rome from bad bonuses. Maybe I'm playing it wrong, or maybe it's just not the right civ for me.
21, Brazil (Pedro II)
Magnanimous is interresting ability, but nearly useless, because Great People are often a small help, and there are only few game changing GP like Adam Smith, Carl Sagan, Wernher von Braun and few others. Amazon is somewhat good, because it can help a lot in creating worthy cities in jungle, but on the other way, jungle blocks you place for other things like farms. Carnival is decent, Carnival project isn't bad either. Battleship is crazily OP, and Minas Geraes, improved Battleship, is godly UU. While I say navy is useless, ships with giant firepower, full damage to cities and range of three are always velcomed. It's perfect unit for wrecking enemy coastal cities. Too bad it often won't save you from enemy armies, because most of your cities will be inland due the rainforest often not reaching to the sea... Together, Brazil creates interresting Civ, but not strong Civ. 20 more to go...
20, India (Gandhi)
India is probably the strongest religious Civ in game. And that's all folks. Both UA offer some interresting religious bonuses, but nothing more. Varu is quite good UU and Stepwell is quite good UI. In the other words, India gets this place for being strong in only one victory path and not offering any versatile bonuses.
19, France (Catherine de' Medici)
I just realised I was overetimating France for a long time, so that's the reason for it's long fall. Diplomatic access actually isn't very important in game, so Catherine's Flying Squadron is one of the weakest UA in game. But Grand Tour isn't. Wonder tourism can be strong if you build a lot of wonders, and doubled wonder tourism will make your Cultural Victory even easier, especially if you have production bonus on wonders of three eras. Chateau is insignificant UI, Garde Imperiale is somewhat good UU. Let's move to the next Civs.
18, Sparta (Gorgo)
Wildcard slot is good, but policy cards are only minor game changers, so it's not that good. Acropolis is good, because both Sparta's and Athens' main target is Cultural Victory. Hoplite can be great early game UU, because +10 combat bonus for at least one adjecent Hoplite is nothing to laugh at. But problem with Sparta is that you either have to be constantly at war - that means to be constantly hated, or let barbarian encampments live to gain enough of enemy units for minor cultural boosts. It's not really bad, it's just not the right civ for me.
17, Athens (Pericles)
Athens are better, because +5% culture boost per suzerain can be good if you manage to keep at least 4 suzerains thanks to using right policies in your wildcard slot. But it's situational, although less than Sparta. Let's move on another point.
16, England (Victoria)
British Museum is great UA to help me with Cultural Victory. Pax Britannica is insignificant to me. Sea Dog is kinda insignificant UU. Redcoat, on the other way, is great UU. Royal Navy Dockyard is kinda fine UD. I think this is good place for it.
15, America (Teddy Roosevelt)
Founding Fathers is one of the worst UA in game. Roosevelt Corollary, on the other way, seems fine, because +5 combat strenght is nothing to laugh at in any era. I don't build many National Parks, because Naturalist costs increddible amount of faith and I build Holy Sites only for my Religious Victories, so I often can't afford him and thus fully use this part of Teddy's UA. P-51 Mustang is horrible, Rough Rider is good, but the best part on 'Murica is the incredible Film Studio with double tourism bonus.
14, Japan (Hojo Tokimune)
Meiji Restoration can be fine and versatile ability, if it's used right. On the other hand, Divine Wind is weak to me. Electronics factory is decent UB and Samurai is fine UU, so I'll place Japan here.
13, Sumeria (Gilgamesh)
Adventures with Enkidu is weak. I'm rarely participating in joint wars, because AI refuses to accept it from me, or it offers it to me in times I just really don't want to fight. And if we eventually fight in joint war, AI is usually doing nothing. Discount on CS armies sounds fine, but CS rarely upgrades their armies in my games so it costs ton of money to make them at least little bit useful. Epic Quest is kinda fine, because Extra Tribal Village bonus is always welcomed. Too bad you only get few more of these things. Ziggurat is kinda fine, because it can give you early game Tech and Civic lead. The best part of this Civ is the godly War Cart. It's seriously one of the most game changing UU in game. But the other civs are better...