As of this writing, the American Veterinary Medical Association hasn't taken an official stance on medical marijuana for pets. However, there have been many successful cases of the use of medical cannabis to help pets with diseases or illnesses.

One interesting study proves the importance of cannabinoids in animals by showing that male European starlings with higher expressions of CB1 receptors sang more to females, and exhibited higher dominance in nesting sites.  In addition, the ailments experienced by aging humans and animals can be quite similar. Some of the human maladies for which CBD’s use has solid scientific research backing include:  

Inflammation, Epilepsy, Fearfulness, Spasms, Rheumatoid Arthritis, Anxiety
Irritable Bowel Syndrome (IBS), Parasitic Infections, Bacterial Infections
Pain, chronic pain management, Nausea, Glaucoma, Skin Problems
Considering the similarity of endocannabinoid receptors in humans and animals, it makes sense that CBD could treat these conditions as effectively in dogs, cats, and other furry or feathery friends