Yes, there is an epidemic of dog bites, certainly in the United States. According to the Centre for Disease Control and Prevention (CDCP), two percent of the population of the United States is bitten annually! One out of every six bites is serious. The rising number of dog bites is linked to the increasing dog population.
We don't have statistics on dog bites for Canada, but as in most things, there is reason to believe that dog bites in Canada cannot be far behind.
And yes, you can make a legal claim for injuries suffered in a dog attack.
In Newfoundland and Labrador we have a Dog Act. The Dog Act effectively imposes what amounts to strict liability on the owner of a dog which causes injury, with no proof of negligence necessary. The challenge then becomes identifying insurance or other assets that can respond to and pay a claim, but the good news is that most people have mortgages and banks required home owner insurance to be carried. Home owner insurance typically covers personal injuries caused by the owner, including by dogs.