One thing to recognize is that each animal is an individual. While there are norms for each species, age, breed, and so on, each animal will have its own set of normal parameters and behaviors.
If you feel that your pet is not him or herself, but he or she is not really sick either, it is wise to check in with your vet to see if an exam is warranted—even if it is just a phone call to touch base.
Ultimately, you know your pet best, and while a description of not himself can encompass a variety of situations, it is best to get your vet's opinion, as animals can be very good at hiding illness until the problem is advanced.
Check-In With the Vet
Your vet can assess vital signs, body temperature, heart rate, and rhythm. He or she will also ask you questions about your pet's habits or recent behaviors that will hopefully aid in finding out why your pet is not acting as he or she normally does. Your veterinarian may suggest some lab work (blood, urine, stool) to investigate further what may be going on. It may be something simple; it may be an early indicator of something serious.
Watching and Waiting
Early detection and prevention are always the best—both for your pet's health and ultimately for the cost of treatment. The wait and see approach is OK for perhaps a day provided your pet is not in pain, still eating, able to relieve themselves normally, etc. Even so, more than 24 hours of being lethargic or depressed warrants at least a phone call to your veterinarian to discuss your concerns.
When It Isn't OK To Wait
If your pet is in pain, won't eat, can't urinate, experiencing bouts of vomiting or diarrhea, please call your vet as soon as possible. These situations can be (or become) quite serious in a short period.