It depends where you are going. Most if not all require your pet to be microchipped with an ISO compatible microchip often before Rabies vaccination to prove that is the animal given the rabies......and on and on.
The worst health certificate I have been involved with so far is to New Zealand, I think. The dog had to have titers for all tick borne diseases, rabies titer, and a few other things that I am not thinking of at this time. Planning it's departure took about 5 months.
So, research your country!!!! Many veterinarians will not do international health certificates due to the hassle and liablity!