Yes, generally a Savannah gets along well with other animals. If you have a dog, it may take a Savannah a little while to adjust if they were not raised around dogs. Other cat breeds that are similarly high energy (Oriental breeds, Abyssinians, Ocicats) seem to work well, as do very patient breeds such as the Maine Coon, Ragdoll, and PixieBob breeds.
A Savannah is not recommended in a house full of birds and fish. A Savannah, like any cat, has strong prey drive and likely will devote much time to devising ways to “play” with caged birds or tanks with fish.