The Pit Bull is first and foremost, a people-loving breed. They are gushingly affectionate towards all they meet, including children and strangers. Because of the selective breeding of the original Pit Bull - to never lash out at a human, despite pain and traumatic injury - the Pit Bull today should be very tolerant of rough handling. This makes them a fine companion for homes with young children. However, as with any breed, dogs and children should not be left unsupervised, and intentional rough handling such as tug-of-war games are discouraged.
The proper Pit Bull should never be human aggressive or fear aggressive. These are seen as serious faults in Pit Bull temperament. The proper Pit Bull should only show aggression towards humans when protecting it's owner from immediate threat. Human aggression in a Pit Bull is a serious issue and must be addressed immediately. Traits such as extreme shyness, fearfulness, and aloofness are also not desired.
(Note: Resource guarding (growling over food, toys, being moved off the couch, etc), while not out-right human aggression, is not something that should be taken lightly. Owners of dogs with resource guarding issues should seek the help of a qualified behaviorist.)
Because the Pit Bull of yesteryear was bred to be the ultimate canine warrior - fighting against other dogs - some level of dog intolerance is to be expected in today's Pit Bull. Not all Pit Bulls will become dog aggressive as adults, but it is something that owners need to be aware of and prepared for. A Pit Bull will often be fine with other dogs until he hits maturity - usually around 18 months of age, but may also emerge as early as 8 months and as late as 4 years. Because dog aggression is usually a genetic trait in these dogs, it cannot be trained out, only managed. While dog aggression should not be seen as a fault, uncontrollable and excessive dog aggression is not desired. More on the topic of Dog Aggression (link here).
The Pit Bull is a terrier breed, and therefore can often have high levels of prey drive. This means small critters such as squirrels, rabbits, even cats, are seen as fun things to chase and potentially kill. However, we have seen many Pit Bulls do well in homes with cats - provided the owner is diligent and responsible in setting both literal and figurative boundaries to ensure the safety of cat and dog. Because of their strength, Pit Bulls should not be left unsupervised around small animals