The most common response to this question is not yes or no, but “why would you want to?”
Well, cats can certainly be trained and there are many reasons you would want to. You can train a cat to stay off kitchen counters, stop scratching the sofa, use the litter box, walk on a leash, accept other cats, stop spraying, ride comfortably in a carrier and even perform tricks.
The key to any behavior modification is reinforcement and punishment. If doing a behavior is rewarding, they will do it again. If it is unpleasant, they will likely avoid doing it again. Just remember that things that motivate a dog might not work on a cat.
You have to find out what your cat cares about. Does your cat crave attention, treats, a certain food, catnip or a special toy? Use the things your cat loves best as a reward for the behavior you desire. What does your cat dislike? Does your cat hate high-pitched sounds, clapping, bells, whistles? Generally, cats don’t like to be startled, so find the noise they think is annoying and use it consistently when they do a behavior you want stopped.
You must never hit your cat, bop them on the nose or use any reinforcement so negative that even worse behavior might ensue. Cats are smart enough to change their behavior with consistent signals from you.
These are some really basic training suggestions. If you cat has a severe behavior problem, please visit your vet. Many times cats act out when they are not feeling well. So the vet is the first stop. And, your vet will be able to suggest specific behavior modification techniques for severe cases.