The extent, to which this is possible or appropriate, depends on the clinical settings and circumstances and the individual beliefs of the treating doctor. Some doctors may feel comfortable with the request while others may not. Though there is no binding but most of the times, the doctor will oblige and pray with the patient.
This request often depends upon the religion of the patient. In Christianity, this type of a request is often made by dying patient and is very important for the patient. If the doctor is not comfortable in obliging this request, he or she at least can sit by his side in silence as the patient prays.
In Islam, it is common for doctors to pray for their patients. Patients may also pray either for themselves or for other fellow patients or even for their family members.
The Hindu religion does not have any specific guidelines on doctors praying together with their patients.

