Drill - a favourite of mine
Benefits: First Strikes (Drill2 and Drill4), FS chances (Drill1 and Drill3). Takes less collateral damage. +10% bonus against mounted units (Drill3 or Drill4, don't remember which, and for most parts irrelevant).
Available for archery, siege, helicopter (gunship being the only one), and armor (tank and modern armor) units, as well as ships. As I don't play much modern warfare, I'll skip gunships and armor here. Also, I rarely give ships Drill, although I can certainly think of cases where it would be good.
So, Archery units: archer, longbow, crossbow. Archers promote to longbows and crossbows.
Longbows' basic duty is to sit in cities, never face combat. Except in the cases where a city I've just captured is attacked (I try to bring a longbow in my SoD so that the newly captured city gets a reasonable top-defender immediatelly). Basic promotion: City Garrison. If a longbow somehow faces combat and gains fourth promotion, I go for Drill line. Garrison-Drill longbow is almost invincible, able to take on many attackers with just the first strikes, but it has to be strong (therefore garrison) to do it.
Crossbows are anti-melee units. Stack defenders, and OK to handle the last spear or whatever in the city you're taking. My promotion line for crossbows is Drill, possibly shock mixed in.
UUs: Skirmisher (Mali), Cho-Ko-Nu (China).
Skirmishers I give Drill almost always, as they're strong enough as it is. Those that gain some XP will later on be upgraded to xbows.
CKN do additional collateral damage. Both Chinese leaders are protective, so starts with Drill1 (and CG1). Thus, 10XP for Drill4 - and Drill4 is the reason to go down the road. One of my favourite UUs, good in the fields, good semi-mopup for city attacks.
Protective leaders may want to go down the drill line with xbows, as 10XP will gain the prize, Drill4. Charismatic too, as the goal is only 13XP. 17XP is a bit high, so without charismatic or protective, the goal is far away and other promotions might be better.
Note that stack-defender xbow that fends off a few axes will end up with high XP easily. And if they are going up the Drill tree, they are less suspectible to collateral damage, thus being even better in their job as stack defenders.
Xbows upgrade to grens and rifles (and machineguns via grens, but I never do that), longbows to rifles. Drill4 rifle is possibly the best stack defender you can get, until Drill4 infantry. I've had an archer->ckn->rifle->infantry unit end up with Drill4 and Combat4 - highest XP it ever got in one turn was 17 (which means it fended off 17 attackers in that single turn, taking minimal damage).
Then there're the siege units.
To begin with, machineguns are different from the rest. They can't attack, do no collateral.. They're defenders, good against rifles, reasonable against infantry. Marines eat them for breakfast. Drill is good for mgs.
Then the rest of the siege units.. Cats suicide. Give them barrage or CR or whatever. They won't live long enough anyway.
Trebs are purely city attack units. CR up to top, usually maces handle mopup.
Cannons may go barrage line (if you mean to use them in the fields, not against a city), or CR line (if you specialize them for city attacks). However, cannons are quite strong against rifles, so I might consider CR cannons against top defenders, then Drill cannons against somewhat softened defenders, then mopup probably with grens. If you have cannons against pre-rifle defenders, I'm not sure if their promotions even matter.. Drill sounds good in that case though.
Artillery is quite similar to cannons.
I'm not going to exact combat mechanics here (there's a good article in war academy, recommended reading if you're thinking about different promotion lines), but in general, Combat promotion is good if that pushes you from "weaker than" to "equal strength" or "stronger than" position. In almost all other cases, first strikes are better. However, Drill1 and Drill3 provide first strike chances, not first strikes. I would say that Drill1 is most often a bit weaker than Combat1, but when you get all the way to the top - to Drill4, it's most often better than Combat4.
Drill also unlocks counter promotions (shock, cover, and so on) just like Combat, so you won't miss those either.
Specialist promotions (garrison, city raider) are useful only in their specialty, Drill is more general. Comparison is thus against Combat, which is an overall promotion as well. It's quite hard to beat the specialist promotions, as they give up to 75% bonus, but then again - when that +75% gives you 99.6% odds (instead of only 90%), I can't see how it would be more useful than generic (Drill/Combat) one - CR is best for units that will take out top defenders in the city, not for mopup units.