Basic, Straight Jabs
Some modern fighting organizations, such as the mixed-martial arts Ultimate Fighting Championship, attempt to make fighting as artful and realistic as possible; however, due to the dangers affecting the hands, they require gloves over the hands. Control is the key to bare-knuckle punching. A simple, straight jab can be an effective bare-knuckle punch. Extreme care should be taken to not throw it as hard as you can, as well as to keep it controlled and straight.
Controlled Hooks
A hook can be an effective short-range punch. Hooks should never be thrown wildly or from afar; they are best used in close-combat fighting. The hook also has an advantage as throwing it from close range causes an aim towards the chin vs. the top of the head, which makes the punch less likely to cause damage to the hand.
Backfist Punching
Backfist punching is a type of punch more associated with alternative fighting arts, such as Muay Thai (where it is currently legal to throw within competition matches). It consists of the hand being thrown at an angle, striking the opponent with the knuckles, hand open and palm facing inward. This punch is particularly risky if not done properly or if the knuckles strike an extremely hard target.
Other Negatives of Bare-Knuckle Punching
Outside of damage to the hand, there are several other reasons why bare-knuckle punching isn't recommended. One reason is that it's difficult to practice effectively and efficiently; it causes punchers to slow down their punches in an effort to accommodate the pain. This can cause your muscle memory to learn to punch at a slower pace and may even affect your precision.