Japan is hands down the best military civilization if you're fighting a
defensive war. They aren'y weak on the offense at all though.
Denmark is really excellent on archipelago and small continents / continents. Relatively solid on other map types too - can often hold a large empire in the polar regions.
Providing there isn't a whole lot of rough terrain on your map, Mongolia can pretty much trample anything in the medieval era and to an extent the renaissance, beneath Keshik hooves. They are a good military civ pretty much all game long.
China is a very solid military civ, perhaps slightly better at defensive wars due to the chukonu than offensive but still very very solid at both kinds of warfare.
In the Ancient-Classical era Greece is a power house, but later on tends to be better at diplomacy.
Siam is great in the medieval era only because they have Narusan's Elephant which is an absolute top tier UU.
Russia is a very solid warmongering civ all the way through the game, but they're versatile - you're not restricted to a military victory as your resource advantage can be turned into a trade advantage.
Arabia is interesting as a later game oil-based warmonger. This is obviously more effective on slower game speeds.
Aztecs are great in the very early game, and pretty solid for the rest of the game as well.
Spain is good on continents / Terra, but not a super war focused civ.
Rome's effectiveness as an early game warmonger is entirely dependant on how much Iron you have access to.
England is a great war civ in the medieval era because of the longbowman (which can be used great offensively because of its range) and is basically the master of the seas. No other civ even HAS a naval UU yet. Here's hoping for a Korean turtle ship UU
Jannissary makes the Ottomans good, and their UA is now a lot better.
I'm yet to see how Germany is, but the -25% discount on unit maintenance is sure to be really useful and help fuel offensive wars.
If you can keep happiness under control and keep the momentum of conquest, Songhai are really great as well.
Overall I would say these are the tiers for warfare:
Top tier:
Denmark
Japan
England
China
Mongolia
Songhai
Mid tier:
Germany
Aztecs
Russia
Greece
Fair tier:
Ottomans
Rome
Arabia
Russia
Siam
Spain
Arabia
Low tier:
Every other civ.