What CQC moves can you do in Metal Gear Solid V: The Phantom Pain?

Combos

You can do a combo up to five hits long by tapping the CQC button in rapid succession. Three hits will knock your average guard from behind and five hits will knock them out from the front. This is the most effective in terms of stun "damage" and it will knock your target out for the longest. It's not completely quiet, so be wary of using it when other guards are nearby. Guards that are aware of you will try to stab you with a knife or hit you with their rifle butt if you come within melee range. If you press the CQC button, Snake will deflect their attack and do his combo normally. Just be sure not to be slow about it.

Disarm

In addition to the combo, you can hold right-click (the button you use to ready your weapon, not sure what it is on consoles) in the middle of a combo to instead take the enemy's weapon and instantly perform a hold-up. This is very useful during [SUBSISTENCE] missions.

Holds

You can perform a chokehold by holding the CQC button when you walk up to an enemy. This will allow you to choke out, kill, or interrogate the target. Choking out is effective at keeping your target unconscious, second only in duration to the full striking combo. Tapping the CQC button rapidly during a choke-out will choke out the target faster, up to roughly half the time it takes just holding the button. You can let go of the CQC button briefly and re-click it and a movement direction together to perform a throw out of the hold.

Up-and-Over and Corner Holds

If you are crouched behind a half-wall, such as stacked sandbags, you can quickly drag a guard on the other side of the wall over to your side and put them in a hold with the CQC button. You have to be directly on the other side of the wall from the guard. If you're standing around a corner and a guard walks up to the corner, you can grab them and hold them securely behind the corner. Just remain still in cover on the corner of the wall and hit the CQC button when the guard walks close enough to issue the prompt.

Throws

Pressing a movement direction and tapping the CQC button at the same time will allow you to instantly perform a knock-out throw. This only leaves them unconscious for a few seconds, however, so be sure to follow-up with something else. This move is fast, and you can chain it together with other guards nearby (you won't be alerted while chaining the moves together as far as I can tell, even when reflex mode is off), so it is effective if you've been spotted by nearby guards and they're about to sound the alert.

Into Walls

If the guard is close to a wall, and you are positioned appropriately and you press the appropriate direction as you push the CQC button, you will throw them face-first into a wall or other large object. This will knock them out longer, but it is still not a safe long-term option.

Hold-Up

Hold-ups are performed when you point a firearm at an unaware guard from point-blank range (three meters or less). Snake will automatically whisper "Don't. Move." and the guard will timidly place their weapon on the ground and raise their hands. Pressing the call button will give you the same options that you would normally get during a CQC hold interrogation. In addition, you can tell the guard to "get down," which will effectively neutralize them indefinitely. However, other guards will help them back up and up the alert level. Also, if you go on combat alert, they'll get back up and retrieve their weapon.

Sometimes, holding up a guard will not give you access to the regular holdup commands - this is because the guard is planning to turn the tables on you. They'll reach for a knife and then spin around and slash you with it. If they hit you, you'll be knocked back and they'll have time to raise an alert. If you can't immediately interrogate a held-up guard, give 'em the old grab and slam for safety

Thanks @twobugs.

Trip

If you are prone and press the CQC button, Snake will perform an arm sweep that will trip enemies. This is not a very effective move overall and it's best to avoid it. It has a very limited application, which is that you've been spotted while prone and you need to buy yourself a couple of seconds. Once you've tripped the guard that spotted you, be sure to stand up or crouch so that you can perform proper CQC.

If you're laying on your back (such as from being slashed from failed hold up) pressing Attack will perform a sweeping kick that ends with you crouched. The effect is similar to the arm sweep. After you knock the guard down you can Aim to perform a hold up.

Thanks @Ampersand. You can turn over by using the roll action (hold sprint and move left and right while prone) or by going prone, then using a weapon to aim behind you -- that will cause Snake to flip over so he can aim in that direction.

The Boot

Standing or crouching over enemies that are tripped or unconscious and hitting the CQC button will kick them while they're down. If they're unconscious or sleeping, this will wake them. If they're not, they'll fall unconscious. I'm not completely sure how long unconsciousness induced in this way lasts.

Goomba'ing

Landing on a guard's head from above will render them unconscious instantly.

Shimmying/Ladder Throws

...you can pull people down to knock them out when they're standing at the top of a ladder you're climbing [by pressing the CQC button]

Thanks @user2357112.