Animals that Kill Snakes
For much of human history, humans have domesticated and trained animals to hunt, track, and kill other animals. Sometimes it is in an animal's nature to do so in defense of the home or to establish its dominance on the property. I personally have owned two dogs, a labrador, and a hound, that have proven to be excellent snake hunters.
While my pets did not get bitten or get an infection or disease from chomping a couple garden variety snakes in half, you must take care to make sure that your household pets are not making this commonplace behavior. One day, they may happen upon a venomous snake and may be bitten by it. Besides, there are plenty of natural predators that will kill snakes not for sport, or to please their master, but for food!
Eagles that Hunt Snakes
The pride of the United States is the Bald eagle, and many varieties of eagle are excellent snake hunters. They use sharp claws and beaks to rend snakes in two, behead them, and pick off meat. While all of us who have had snake problems on their property love the idea of this, eagles and other carnivorous birds eat a plethora of other animals and will likely not solve your snake problem in their own.
African Honey Badgers
While they look like somebody stretched a skunk out like a string of taffy, the honey badger of africa is an extremely skilled hunter and can handle some of the most dangerous snakes with expert technique. While it is not legal to own a honey badger in the United States, it is even more difficult to train one of these creatures to hunt snakes exclusively.
The mongoose is a small to medium sized mammal with a devilish stare and a bite that is certainly more dangerous than its bark. You won't find these in the continental United States, but in Puerto Rico and parts of Hawaii. They are proud solitary hunters and rarely back down from a fight. While fascinating creatures, they are not going to solve your snake problems in the United States for you.