Yes. And most of them are in use whenever it's possible. New ones are constantly being developed, and everyone looks forward to the day when it may not be necessary. Computer simulation, tissue culture, and other methods are the most common.
BUT. There are still situations where animal testing is the best, most accurate way to simulate a human living system. For more information, Google the concept of the "Animal Care and Use Commitee", a body that most research companies and universities use to determine whether a particular experimental treatment is adequate for use on animals, or if a better method is available.