In some countries, including the United Kingdom and Australia, yes. In those countries requiring certification, Assistance Dogs International is usually the recognized certifying entity.
In other countries, including the United States, no.
In any case, certification should be done by someone qualified to evaluate service animals (not a regular dog trainer), and it should be based on an evaluation performed in person and in a wide variety of situations.
"Registration" over the internet, accomplished by filling out a form and paying a fee (usually $40-$50), does not qualify a dog as a service dog. It doesn't hold up as proof a dog is a service dog. It's just another rip-off. Save your money and get a real evaluation.
Note: A CGC (Canine Good Citizen certificate), CGN (Canine Good Neighbor certificate), or any of the Good Citizen Dog Schemes certificates do not make a dog a service dog. While any service dog should easily pass a citizenship test, not all dogs who pass the citizenship test will have sufficient training or an appropriate temperament for service work.