Ottomans: Janissary (Musketman)
Warlords and BTS only. The Janissarys advantage is a 25% boost against melee, archery and mounted units, making it a great all-round unit for its time. It is pretty much effective against all previous era units (with the big exception of siege units), so you can potentially put some serious hurt in your enemies.
In order to get as much use out of Janissaries as possible, you need to look for ways to get to Gunpowder early. You might even want to make a beeline for it, either through the northern path (Maths -> Currency -> Priesthood? -> Civil Service -> Paper -> Education) or the southern path (Metal Casting -> Machinery & Monotheism -> Monarchy -> Feudalism -> Guilds) in the tech tree. Different lightbulbing strategies are available (with Great Merchants for the southern path and Great Scientists for the northern one), so you don't have to self-research everything. Strictly speaking, it may not be necessary to do a beeline, but it's probably the best way. The point is to get to Gunpowder before your enemies are even close to it, and rapidly exploiting this opportunity gap by building, whipping and possibly drafting as many Janissaries as you can to use against them. To be able to draft, you would need to pursue the northern path and probably research Liberalism first to grab Nationalism as the free tech, before actually researching Gunpowder. It is a slight diversion, but it may be worth the delay if your empire does not have the capability to build or whip enough Janissaries in time to give you a real edge, as often is the case.
Once you have them, Janissaries are quite a fearsome force in the medieval battlefield. They have no hard counter, so the best bet your enemies might have is to promote their units with Pinch, which requires Gunpowder in Warlords. Knights with Pinch, however, are a good counter to Jannissaries, as are regular musketmen (against whom Janissaries have no advantage whatsoever), so once your enemies have Gunpowder as well you may find your edge disappearing. If they manage to get to Chemistry, which isn't that far away, this UU is practically obsolete. Janissary stacks are actually relatively vulnerable to siege units (and the associated collateral damage) as well, since they don't get any bonuses against these. But unless you're playing MP, this shouldn't be a big problem. The AI does not generally build many catapults.
Also take note that Janissaries may not be the best city-taking troops you can get, since they do not have access to City Raider promotions. Needless to say, if you're relying on them as the backbone of your army, you still need to bring siege weapons along if you hope to grab some enemy territory. Given the fact that they are not actually very different from the conduct of normal campaigns of the time, Janissary campaigns might still be slow going, so don't be surprised if you don't manage to knock out more than one enemy with them, even with your best efforts (assuming you're playing on the higher levels). Hence, the emphasis is again on getting them as early as possible so as to enlarge the window of opportunity that you have.
Overall, without the mobility of the Musketeer, this UU is quite situational and, to an even higher degree than the former, requires some long term planning in the early game to be put to good use. It is probably better the lower the difficulty you play on, since you would be more likely to out-tech the AIs and get to Gunpowder much earlier than them.