The truth is that it is prudent to be wary of any dog until you know it. Lately discussion around pitbulls seem to be rather polarized - with the 'anti-pitbull camp' claiming that the breed is incorrigibly vicious and blood thirsty - and the 'pro-pitbull camp' literally touting photos of full grown pitbulls posing with sleeping babies.
Having worked with over a thousand dogs in the past six years, the ones that have bitten me hard enough to leave a mark are: two pitbulls, a cocker spaniel, a rat terrier, a pekinese, and a doberman. My son has been bitten by a german shepherd, a border collie and a cocker spaniel.
The dogs that I have known to inflict serious bites on my clients or employees (i.e. enough to send someone to the hospital) are: cocker spaniels and portuguese water dogs.
The only breed I can say that I am more than usually wary of is the cocker spaniel. Statistically, they are not all that likely to inflict a maiming bite, but I have known them to land several people in the hospital and I consider most of them kind of unstable. The 'official list' of breeds that are likely to bite is topped with dachshunds, jack russell terriers and chihuahuas. While it is true that none of those breeds is known for often inflicting life-threatening bites, they are more than usually prone to bite and it is worth bearing in mind that any dog bite can maim depending on wear the dog bites, with how much force and whether the dog twists its head and body while biting.
My own experience of pitbulls is that most of them are lovely, level headed suitable pets. However, the breed is popular with a group of people who raise them for fighting and breed for qualities sought in fighting dogs. So it helps to know where the dog came from. Also, even run of the mill non-fighting pitbulls seem to have some traits that are worth bearing in mind. If they are pushed beyond their tolerance of frustration, pain or fear, pitbulls tend to react explosively. (Pushed beyond those limits, almost any dog will react, it is the vehemence of the pitbull's reaction that sets them apart.) Virtually all dogs give non verbal signs that they are stressed and want to be left alone, but pitbulls seem to move through those signs a lot faster than other breeds. Also, when they explode, pitbulls tend to do so very forcefully (on account of their size and strength) and they tend to take longer than most breeds to cool off again and break off their attack.
Bottom line: I let my kids play with pitbulls if I know the dog's owner and I know the dog is well socialized and trained. I also ensure that I am near enough by to watch my kids with dogs and that I can intervene if I need to. When I work with pitbulls, I treat them like any other dog - i.e. I assume they may bite, until I have seen them under a variety of situations. And, at the end of the day, I accept that still they may bite - simply because they are dogs, not because they are bad.
I would link to some of the studies on breed specific human bite statistics, but it is very hard to find quality studies that take into account whether the breed of the dog that bit is accurately identified, whether the statistics are adjusted for the prevalence of the dog in population and whether the bite was made in the course of police action, etc. Almost all of the data that is out there has been compiled or funded by one side or the other of the pitbull debate. But, no matter how you slice it, you are more likely to wind up in an ER because of a bedroom slipper than because of dog. And you are more likely to be killed by a refrigerator tipping over on you than to be killed by a dog.