Most veterinarians do not charge for "suture removal" appointments, so the only requirement on the part of the pet owner is the time scheduled for the visit. For busy people, the appointment might seem like an extra expense of time, however this is a great opportunity to visit with your vet about how your pet did post-operatively (excessive grogginess? Any vomiting?) and perhaps make notes about any future anesthetic or surgical procedures and what would be best for your pet.
This is also a good time to discuss any concerns you had about the surgery, what to expect during the healing process, and any behavioral aspects or problems in the future to watch for.
If you do elect to remove the sutures yourself, call your veterinary office and let them know so that they can make appropriate notes in your pet's health record and answer any questions that you may have.