The majority of dog breeds age more or less consecutively and can be considered "senior citizens" after age seven. In some breeds, longevity is limited by breed type and one might expect the aging process to accelerate. Take this into account when judging your dog's behaviors.
The older dog requires a much more aggessive veterinary presence than does the young dog. No more than six months should pass between visits to your veterinarian. Between visits, go over your dog carefully at least once a month to detect small growths, mammary swelling, tooth tartar, ear problems, weight loss or gain (sudden) etc. Do not hesitate to visit your veterinarian if you discover anything that is not normal!
The older dog may, just as in humans, suffer from reduced visual capacity, hearing loss and cognitive deficiency. Dogs acquire cataracts and may react to the gradual loss of sight with behavioral changes. If a dog begins to lose its hearing, s/he may begin to bark more frequently. Lameness due to arthritis or hip problems may occur. All sorts of behavioral and physical problems can accompany aging in the domestic dog.
Be more patient with your older dog. Incontinence is a symptom of aging and should not be met with punishment. The older dog may sleep more and be less tolerant of children, kittens, puppies, etc. Remember that this dog has been a good friend throughout its lifetime. Don't expect your dog to perform as it did when it was younger.
Diet is quite important in the older dog. There are several premium dog foods expressly intended for these dogs. Give your dog the best food you can afford. Exercise him/her within parameters s/he is accustomed to. Visit your veterinarian frequently. The best gift for an older dog is the gift of loving compassion and long term commitment.