The famous sabertooth cat is well know because of the enormous numbers of skeletons being found in the tar pits of Bracho la Brea, but sabertooth cats have been found in almost the entire world. The family lasted longer than any dinosaur family did, so you might say sabertooth cats were probably the most successful hunting design ever created in nature.
The largest sabertooth cat was Smilodon populator, from South-America. Its saberteeth were 30 centimetres long, it needed to open its mouth more than 90 degrees in order to be able to bite.
The teeth weren't for grasping and holding prey, for this they were too weak. They would break if they came in contact with bone, so Smilodon used his strong front legs to bring down the prey.
When the prey was on the ground, the sabers were used to kill it. They where perfectly desigend to slice through the blood vessels in the neck and they close off the windpipe as well. The cat needed to bite only once and the prey was dead.
Sabertooth cats preyed mostly on large hoofed animals, and maybe rhino's and hippo's. One kind of sabertooth cat, Homotherium, seems to have been specialized in young mammoths.
Unlike many other cats, Smilodon hunted in packs. Fossils have been found, and some Smilodon specimens show serious injuries. The injuries would have made the cat unable to hunt, but the injuries had healed. This suggests that the cats may have been feeding from kills made by others, and were living in a group. Unlike almost all other cats (Lions are the only present day cats who live in a group.) sabertooth cats where social packhunters. It were probably the females that hunted prey, and the group was ruled by one dominant male, just like lions do. The fossils suggest that different groups had their own territory.
Although it's been said that if there had been no humans, the sabertooth cat would still be around today, its unlikely that they became extinct because of early man. Humans did not have the right tools yet to drive a succesful species towards extinction. By the way, in South-America the sabertooth cats became extinct before humans reached the continent. Instead being overhunted by humans, the mammoths and sabertooth cats became extinct because of a climatic change.