Each Civilization has it's own unique units (otherwise this game would be REALLY boring), some with their own unique names. Also, there are some unit types availiable to all civilisations but are best for maybe one or two Civ's. These are called 'Royal Guards'. Here they all are:
The Spanish: The Spanish Unique units are the Lancer (Cavalry), the Roderlo (infantry) and the Missionary (priest). Lancer are specially trained to slice through infantry, and have reasonable health. The Roderlo is a fast moving buckler infantry, with a small bonus attack vs Cavalry, but poor health. The missionary is just a priest on a donkey really. the Royal Guards are the Tercio Pikeman (tho only pikeman who can be upgraded past veteran in the game), the Garrochista Lancer, and the Espada Roderlo.
The British: The British Unique Units are the Longbowmen (infanrty) and the rocket (artillery). Longbowmen have the longest range in the WHOLE game and have a slight atatck bonus vs Infantry. They cannot be upgraded past veteran UNLESS you get a home city shipment allowing them to be. Rockets are a factory-produced artillery unit that has a worse health and attack then the other factory-produced artllery, but they make up for it by having an immense ship attack (4.5X bonus if you get an arsenal upgrade (The one that looks like fire), otherwise 3X bonus) and a greater damage wave, meaning it hurts more men when it attacks. Their Royal Guards are Redcoat Musketeer and King's Life Guard Hussar
The French: The French Unique Units are the Courer de Bois (Settler) and the Cuirassier (cavalry). Courer de Bois are the best settlers in the game, as they can double as infantry in dire situations. They also cost 20 food more than average, non-dutch villagers. The cuirassier is the best possible-to-buy-infinately (as in cavalry that can be bought from stables) in the game. When Imperial, their health is over 1000 (with home city shipments) and their attack is joint second best with the British and Ottoman Hussars. their Royal Guards are the Gendarme Cuirassiers (special note: In my experience of this game, when playing against the French I always hear myself yelling "OH GOD NOT GENDARMES!". they are, in other words, Immense) and the Voltigeur Skirmisher.
The Portuguese: The Portuguese Unique Units are the Organ Gun (artillery) and the Cassador (infantry). Organ guns are a sort of old machine gun, in qhich it shoots several bullets at once, killing at least 2 infantry units in one usually. The Cassador is an infantry version of the Uhlan (you'll read about them in the German section). They have poor health but a good attack, especially against infantry. Their Royal Guards are the Guerreiro Musketeer and the Jinite Dragoon (which work VERY WELL against Gendarmes, just so you know.)
The Dutch: The Dutch Unique Units are the Ruyter (cavalry), Fluyt (ship) and Envoy (recon Unit). The Ruyter is a weak anti-cavalry unit that is only decent against cavalry. This isn't surprising as the Dutch focus mainly on a economy, due to banks. They're best as an ally. Envoys are very weak units that have a good Line of Sight. DO NOT use them for combat. If you do, you'll see why. The fluyt is like a galleon but faster, most resistant to attack and stronger all round. Their Royal Guards are the Nassau Halberdier and Carabineer Ruyter.
The Russians: The Russian Unique Units are the Strelet (infantry), Cossack (cavalry) and the Oprichnik (cavalry). Due to Russian building their units in large batchets, Strelets are useful. They are also cheap. But they are EXTREMELY WEAK. Their starting health is 72 with an attack of something like 7, but due to their immense amount of number you can make at a time (10 at one time in one blockhouse) they are awesome for rush attacks. The Cossack is alot like the Cuirassier, only weaker. They are still a strong cavalry unit though. The oprichnik is the only raid unit in the game, with good health, decent attack and an amazing siege attack (for a cavalry unit). If you get, say, 20 and justattack the enemy resource building or outposts or whatever, you should be able to destroy them quite easily, as when Imperial their Siege attack is 126, which is the best of any non-artillery unit. Their Royal Guards are the Pavlov Grenaider and the Tartar Cavalry Arhcer.
The Germans: The German Unique Units are the Doppelsoldner (infantry), Uhlan (cavalry), War Wagon (cavalry) and the Settler Wagon (Settler). The Doppelsoldner is a strong-in-health unit that has a weak but wide attack, injuring several enemies at once. If you have several Doppelsoldners in the same area they will kill alot more enemies. The Uhlan is a poor health but strong atatck unit, that comes free in home city shipments but can also be trained in the stables. They have the best stable-trained cavalry attack in the game at Imperial level. Settler Wagons cannot be trained (unless you get a card which allows up to 20 to be trained from mills), but can be recieved by home city shipments. They are the best resource collecters in the game, better than Courer de Bois, but have a poor attack. The Royal Guards are the Prussian Needle Gunner Skirmisher and the Czapka Uhlan.
The Ottomans: The Ottoman Unique Units are the Janissary (infantry), Abus Gun (artillery), Spahis (cavalry), Great Bombards (artillery), Galley (ship) and Imam (priest). The janissary is the only infantry availiable to the Ottoman, and is a more powerful musketeer. The Abus Gun is an anti-infantry artillery unit that isn't too expensive but works well in numbers. Spahis are EASILY the best cavalry unit in the game, but can only be bought through home city shipments (they cost 200 food each). They upgrade automatically when you go up an age, and their health is around 1400 (with no arsenal upgrades) at Imperial and their attack easily rivals an Imperial Gendarme, but they are limited. Great Bombards are slow moving slow loading artillery units that are so powerful it hurts to think about. At Imperial, about 3 can destroy a Town Centre in one, maybe 2 shots. Galleys are pretty much Fluyts in Ottoman form, and Imams are just a Muslim Priest (as Ottomans are Muslim). heir Royal Guards are the Gardener Hussar and Baratcu grenadier.
The best civilisation for Unique Units qould probably be the Ottoman, as they have the most, but the best Royal Guards ARE NOT OTTOMAN FOR ONCE, but I will give that to either the Spanish (as they are very anti-cavalry and they respect pikemen, unlike the rest of the civs), the British (as their Redcoats in number are very, VERY hard to stop) or the French (as their Gendarmes are just fantastic).