Owners of Savannahs say that they are very impressed with the intelligence of this breed of cat. An often noted trait of the Savannah is its jumping ability. Savannahs are known to jump up on top of doors, refrigerators and high cabinets. Some Savannahs can leap about 8 feet (2.5 m) high from a standing position. Savannahs are very inquisitive, and have been known to get into all sorts of things. They often learn how to open doors and cupboards, and anyone buying a Savannah will likely need to take special precautions to prevent the cat from getting into things.
Many Savannah cats do not fear water, and will play or even immerse themselves in water. Some owners even shower with their Savannah cats.Presenting a water bowl to a Savannah may also prove a challenge, as some will promptly begin to "bat" all the water out of the bowl until it is empty, using their front paws..
Another quirk Savannahs have is to fluff out the base of their tail in a greeting gesture. This is not to be confused with the fluffing of fur along the back and full length of the tail in fear. Savannahs will also often flick or wag their tails in excitement or pleasure.
Vocally, Savannahs may either chrip like their Serval father, meow like their more domestic mother, or do both, sometimes producing sounds which are a mixture of the two. Chirping, when present, is observed more often in earlier generations. Savannahs may also "hiss"—a Serval-like hiss is quite different from a domestic cat's hiss, sounding more like a very loud snake hiss, and can be alarming to humans not acquainted to such a sound coming from a cat.