DNA profiling is most commonly used to determine the sire of a litter.
AKC DNA profiling is mandatory in some circumstances (eg. frequently used sires, multiple sires program), voluntary in some circumstances, and the result of kennel audits in others. There is some more information about it at
http://www.akc.org/dna/index.cfm
Note that DNA profiling cannot be used to determine the presence of genetic diseases, nor can it determine the breed of dog (or indeed, whether or not a dog is purebred).