There are eight possible vigor combinations in BioShock: Infinite and using them can increase their usefuleness in combat. Some of the vigors (like for instance MURDER OF CROWS or SHOCK JOCKEY) may seem like they have identical use with only a different visual effect, but that's wrong. If they use only them they may seem similiar, however if combine them together the final effect will be much more deadly. Vigor combinations are almost a requirement if you're going against many enemies at the same time, because they will allow you to get rid of a lot of hostiles in one swoop. You should also know that testing all of these eight combinations will allow you to unlock the Combination Shock achievement/trophy. Check the table seen below for a complete list.
Combination 1: BUCKING BRONCO + CHARGE
Instruction: Use charge on a target that's currently in the air (as a result of using bucking bronco) in order to inflict major damage and to push the enemy away.
Combination 2: MURDER OF CROWS + DEVIL'S KISS
Instruction: Hit the hungry crows with a devil's kills and you'll create more powerful burning crows!
Combination 3: BUCKING BRONCO + DEVIL'S KISS
Instruction: Send the devil's kiss to the area affected by the bucking bronco's and it will divided into several grenades, injuring more enemies at the same time.
Combination 4: MURDER OF CROWS + SHOCK JOCKEY
Instruction: Hit the hungry crows with a shock jockey and you'll create more powerful electric crows capable of electrifying your enemies.
Combination 5: POSSESSION + SHOCK JOCKEY
Instruction: Hit a possessed enemy with a shock jockey and he'll electrify all other opponents standing next to him.
Combination 6: DEVIL'S KISS + CHARGE
Instruction: Charge at a person set on fire with the devil's kiss and that enemy will explode!
Combination 7: POSSESSION + DEVIL'S KISS
Instruction: Hit a possessed enemy with a devil's kiss and he'll set on fire all other opponents standing next to him.
Combination 8: UNDERTOW + SHOCK JOCKEY
Instruction: Enemies soaked down with undertow receive more damage from shock jockey and the electric current can also affect other nearby opponents.