Doctor

A doctor (医者), is a person, or animal (as in the case of Tony Tony Chopper), who practices human biological medicine. A doctor is usually a necessity for sea travel, and they are known as a ship's doctor (船医).

One Piece
Doctors are relatively essential members of any crew, whether it be Pirate, Marine or any crew in between. One who is skilled in medicine and health care is necessary in order for the crew to survive to harshness of the sea. Doctors are usually required to heal wounds from battles, or prepare medicine for sick members.

In terms of Luffy's crew, the issue of having a doctor was first brought up in the Arlong arc, when the doctor of the town, Dr. Nako, said they really needed a doctor, after patching up Zoro's wounds. Luffy said it was a good idea, but they needed to find a musician first.

After the Drum Island arc, Tony Tony Chopper joined the crew as the ship's doctor (although, Luffy originally wanted him because he was a "cool monster that can change into seven forms"; Sanji joked saying he was the "emergency food supply"). Since then, Chopper has fulfilled his duty as a doctor, patching up wounds from battle, and using his knowledge of medicine to the crew's advantage.

Due to the Rumbar Pirates' doctor being killed in battle, the crew had no chance of saving themselves from the poison they were afflicted with, which led to their destruction. This is prove of how much a doctor is crucial in a crew.

Trivia

 * Despite the essential role they played, pirates rarely had a doctor on board their ship as it was mostly commerical and military vessels that carried a doctor. Even when a doctor was at hand, the standards of medical practice were not as they are in the modern world. Most limbs or lives were lost simply because of the crude methods often used on a patient. Thus, sickness and diease was often common within pirate crews and even basic standards of living were not always on par with crews on board legal vessels.