We don't know exactly what causes diabetes in dogs, but there's some excellent research being done on the question now.
Regarding causes in dogs, genetic predisposition has definitely identified keeshonds and samoyeds, with others who appear to be significantly susceptible.  Middle aged to older dogs (5-12 years old--uncommon under the age of 3 years), and females versus males predominate.
As Dr. Rand noted, lifestyle is also a factor.  Every informal poll taken at canine diabetes message board showed that most dogs were overweight at diagnosis.
Current research into canine diabetes finds no evidence of the Type 2 diabetes known in humans.  Most dogs are what's termed Adult-onset IDD, meaning they are dependent on exogenous insulin for control of their diabetes, which did not occur until some point in their adulthood.
Pancreatic cells are either deficient due to congenital predisposition (breeds who are significantly susceptible), or lost/destroyed through pancreatitis or immune-mediated beta cell destruction.
Until recently, antibodies which interfere with a dog's receptivity to exogenous insulin therapy were considered rare. This research finds antibodies present in a significant segment of newly-diagnosed (insulin-naive) dogs. They conclude that canine diabetes is much like human adult latent autoimmune (Type-I) diabetes. 
In some cases, it's another medical condition or medications that can cause diabetes:
With instances like this, there is a possibility that controlling or ending the primary problem (spaying an intact female, stopping steroid meds, getting Cushing's controlled, etc.) may mean that the diabetes won't be permanent.
- ↑ Dog Breeds Susceptible to Canine Diabetes-Caninsulin. Intervet.
- ↑ Rand, J., Fleeman, L., et. al. (2005). Canine and Feline Diabetes Mellitus: Nature or Nurture?. Centre for Companion Animal Health, School of Veterinary Science, The University of Queensland, Brisbane 4072, Australia.
- ↑ Catchpole B, Ristic JM, Fleeman LM, Davison LJ. (2005). Canine diabetes mellitus: can old dogs teach us new tricks?. Diabetologica.
- ↑ Managing Diabetes-Better Medicine-E-Newsletter. Intervet (June 2006).
- Primary & Secondary Canine Causes Vetsulin
- Familial Insulin-Dependent Diabetes Mellitus in Samoyed Dogs Susan E. Kimmel, DVM, Diplomate ACVIM, Cynthia R. Ward, VMD, PhD, Diplomate ACVIM, Paula S. Henthorn, PhD and Rebecka S. Hess, DVM, Diplomate ACVIM, 2002, JAAHA
- Canine and Feline Diabetes: Nature or Nurture? Rand, Jacqueline, Fleeman, Linda, et.al., 2005, University of Queensland-causes of diabetes in cats and dogs