BREAKING NEWS

Is there anywhere that service dogs are not permitted?

Generally guide, hearing and service dogs are permitted to accompany their disabled owner everywhere members of the public are allowed, but there are a few exceptions. For example, a member of the public would be permitted in the dining area of a restaurant, but not in the kitchen. Therefore, a guide dog would be permitted to accompany his disabled owner in the dining area of a restaurant.
It is also an important distinction to note that it is the handler who has access rights and not the dog. A guide dog without his blind handler has no particular access rights of his own and neither does a hearing dog or other service dog without his disabled handler.
"Under the Americans with Disabilities Act (ADA), businesses and organizations that serve the public must allow people with disabilities to bring their service animals into all areas of the facility where customers are normally allowed to go. This federal law applies to all businesses open to the public, including restaurants, hotels, taxis and shuttles, grocery and department stores, hospitals and medical offices, theaters, health clubs, parks, and zoos." -- U.S Department of Justice.
For clarification, contact the U.S. Department of Justice's ADA Information Line at 800 - 514 - 0301 (voice) or 800 - 514 - 0383 (TTY)
In the U.S., according to the Department of Justice's Business Brief concerning Service Animals, business owners/managers can ask 2 specific questions. 1) Is this a service dog required because of a disability? and 2) What task(s) is the dog trained to perform? If these questions are not appropriately answered, the business may exclude the animal, but not the person.
Though service animals of all kinds can legally accompany their disabled handler almost anywhere the handler goes, they can be excluded from areas where their presence would constitute either a fundamental alteration of goods and services available for all or a direct threat to safety. Examples where a service animal might be excluded include:

-Sterile rooms, such as operating rooms, some areas of emergency rooms/departments, some ICU rooms, some ambulances, some delivery rooms (on a case-by-case basis)
-Clean rooms where microchips are manufactured
-Places where food is prepared (though they cannot generally be excluded from dining areas where food is present) (by order of most health departments)
-Open air zoological exhibits, such as open air aviaries (at the zoo's discretion)
-Churches (at the church's discretion)
-Native American Tribal Council Chambers (at the council's discretion)
-Federal Courts (at the judge's discretion)
-Jail or prison cells (at the discretion of the facility director)
-Private clubs (at the club's discretion)
-Private homes (at the home owner's discretion)
So far, this discussion is centered entirely on laws of access in the United States of America. Other countries will have their own laws in place regarding the access rights of individuals accompanied by a service animal.