In general, the cost of pet adoption and the cost of healthcare for an adopted pet is not tax deductible.
However, Adoption fees that are paid to pet shelter may be considered a donation to the pet shelter and may be tax deductible.
You can include in medical expenses the cost of a guide dog or other animal to be used by a visually impaired or hearing-impaired person. You can also include the cost of a dog or other animal trained to assist persons with other physical disabilities. Amounts you pay for the care of these specially trained animals are also medical expenses.
Except for the care of guide dogs for the seeing-impaired or hearing-impaired, or for other animals specially trained to assist persons with physical disabilities, you cannot include veterinary fees in your medical expenses.
source - IRS publication 502 - http://www.irs.gov/publications/p502/ar02.html