Favorite UU of Each Era

Ancient - Maori Warrior (beat out Jaguar because it isn't quite as terrain dependent)
Classical - Mohawk Warrior (although terrain dependent they are quite brutal combined with UA)
Medieval - Berserker (Had a lot of fun playing Denmark!)
Renaissance - Minuteman (Always fond of the scout and this is it's bigger, meaner brother)
Industrial - Comanche Riders (haven't played Shoshone this far but I got several of them from Military CS allies in other games and they are quite good)
Atomic - Zero (barely beat out of the B-17 but freeing up my Oil and devastating enemy air trumps stronger bombers for me)
Great Person - Great Admiral (oddly enough, his oft insulted ability has saved my experienced ships vs overwhelming AI numbers quite a bit - even Faith purchases a few to just spam the heals when clearing out Carthage a few games back)

Ancient : Atlatist. Cheap, no Archery, go through hills.
Classical : Mohawk Warrior. No Iron, bonus fighting.
Medieval : Chu-ko-Nu. Free logistics.
Renaissance : Ship of the lines. Extra Sight.
Industrial : Hussard. Extra Sight AND Extra Movement.
Atomic : B17. Free upgrade.
Great Person : Merchant of Venice. Money is the sinews of war.

Barghaest said:

Great Person - Great Admiral (oddly enough, his oft insulted ability has saved my experienced ships vs overwhelming AI numbers quite a bit - even Faith purchases a few to just spam the heals when clearing out Carthage a few games back)

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Great Admiral is good on water based map (including continents) since it can enter ocean and deep water right away... so it's good for scouting because it will take a while to get to Astronomy. just watch out for barbs.

njmfff said:

Great Admiral is good on water based map (including continents) since it can enter ocean and deep water right away... so it's good for scouting because it will take a while to get to Astronomy. just watch out for barbs.

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Even better for Korea who otherwise have to wait for navigation or have to send out land units.