This is not a super insightful list. I play a lot of Civ 5, but there are some civs that I've played more than others so this is all based off of my personal experiences. The list is longer than 5 but I prefer to warmonger in my Civ 5 games so I apparently have a lot to say. Also I play on Prince mostly...
1. Keshik
The most godly UU of them all, although Camel Archers come very close. To me, the additional movement point matters more than the additional attack power, as that allows the Keshiks to better maneuver and strike where needed. This is an advantage that's hard to quantify but it's there!
2. Camel Archer
Similar to the Keshik, but trades a movement point for more attack power. Honestly I probably should fold the two units into the #1 spot as they're both just really good, for mostly the same reason and I would enjoy using either when given the chance.
3. Longbowman
Longbowmen are basically the Rocket Artilleries of their era; high firepower, standard mobility, 3 attack range and can attack after moving. They don't require any strategic resources, so you can spam them quite a lot!
4. Ship of the Line
Frigates are already pretty solid, so how about a Frigate that has more attack power and more vision so that it doesn't necessitate a spotter or scout? That's a Ship of the Line. In tandem with some Privateers or Caravels, you can take out enemy cities and enemy navies very quickly. Though most of these reviews are just for the units by themselves, the +2 movement bonus to ship units from England's UA also helps Ships of the Line get the first strike.
5. Horse Archer
A very capable ranged unit that's available very early. Doesn't suffer from big movement penalties and doesn't require Horses like the Chariot Archer, so it can be spammed quickly. It's just as strong as a Chariot Archer, but not being constrained by terrain and resources works out quite well (also having bonus promotions is nice).
6. Chu-Ko-Nu
I want to be able to like the Chu-Ko-Nu more, but to me the Logistics bonus is a little awkward. With only 2 movement points, the Chu-Ko-Nu would have to stay in place in order to make 2 attacks and it doesn't have the ability to siege cities safely like the Longbowman does. Generally I prefer to be able to kite with or rotate my ranged units when needed, and Chu-Ko-Nus are a little better there (they can move after attacking thanks to Logistics), but I still prefer Keshiks/Camel Archers/Longbowmen with that in mind.
7. Impi
Without Ikanda bonuses, the Impi get an additional ranged attack before attacking and a bonus against gunpowder units. The additional ranged attack is awesome, for sure, so Impis are still better Pikemen, which are decent for melee units. With Ikanda bonuses involved, Impis start becoming absolutely terrifying in open spaces and unit vs unit combat. 3 movement double attacking melee units that don't really care about ranged attacks? Yeah that's pretty awesome.
With that said though... Impis are still melee units. Melee units have some pretty nasty problems that ranged units don't have to worry as much about (more details spoilered for length).
I keep some melee units around since I will need them in order to actually capture cities. But in my experience, when it comes to survivability, damage output and efficiency, ranged units of similar tech tier are going to perform much better than melee units will in those categories.
8. Battering Ram
+300% attack power against cities is no joke, and since Battering Rams are melee units, they can crush and capture in one move. They're also available very early on in the game; in fact it's technically possible to get a "free" battering ram from a goody hut (you didn't really need a Warrior did you?). However they can't attack units normally (can counter-attack though) and they're melee units.
9. Siege Tower
Siege Towers make a lot more sense design wise than Battering Rams do... but to me they're not quite as fun, nor are they available quite as quickly! They fulfill the same role that Battering Rams do though. I think I'd much rather have a Battering Ram or a Siege Tower over a Catapult when it comes to taking cities.
10. Jaguar
Jaguars are actually pretty cool. They aren't hindered as much by jungles and forests when it comes to combat and mobility, and they heal hit points afer killing an enemy unit. So compared to other melee units, Jaguars aren't as impacted by terrain and don't grind down quite so fast. They also replace Warriors, and their bonuses are promotions that pass on to upgraded units, so it's actually great to make a few Jaguars and have Musketmen/Riflemen running around tirelessly. They're good for unit vs unit combat, but still not so good for taking cities.
Man an awesome melee unit would be:
- Can move after attacking
- Ignores Zone of Control
- Ignores terrain penalties like Scouts do
- Has at least 4 movement points
- Can heal on kill like Janissaries and Jaguars do
- Has March
- This is extra, but only spends 1 movement point to embark or disembark
I only put 1 sea unit on my list, but honestly sea warfare isn't a big deal until Privateers/Frigates, when Ships of the Line show up. Dromons I like using, and though I haven't put Sea Beggars to use that often they do have a very neat set of abilities.
Also, looking through the Civ 5 wikia, War Chariots are actually just as strong as Horse Archers and Chariot Archers. But they also have +1 movement and don't require horses! So I think I will try warmongering with Egypt in the future. War Elephants are also pretty good! They do have -1 movement compared to Chariot Archers, but they're more like Composite Bowmen that have +1 movement and are available earlier (War Elephants are in fact as strong as Composite Bowmen and don't require Horses either!).