There are lots of different types if service dogs, below are some examples;  

Guide dogs ~ guide a blind person or visually impaired person.
 

Hearing dogs ~ alert deaf or hearing impaired person to certain sounds.
 

Mobility SD’s  ~ Helps a disabled person have a more independent life. Helps a person with balance or counter balance and also helps them move forward. Helps pull the wheelchair, helps you transfer from the wheelchair to other locations, helps with undressing, opens and closes doors, picks up items dropped, pays at cash registers  and a whole lot more. There is no end to the many tasks they can be trained to help a disabled person with.

Some other names for mobility service dogs.

Wheelchair Dogs

Helper Dogs

Assistance Dogs

Psychiatric ~ are trained to assist persons living with psychiatric disabilities ; such as grounding them during a panic attack.

Medical Alert ~ Alerts person to a medical conditions before it happens: such as low or high blood sugar, seizures and many other types of medical conditions.
 

Medical Response ~ response to a medical conditions, like getting help, calling 911 or helping the person up.