​What most people consider to be the traditional martial arts uniform is actually a fairly recent invention.  Jigoro Kano, the founder of Judo, developed the dobok in the early 20th century to standardize the clothing worn by students, and to ensure that it would be durable enough to withstand training.  It has since been adopted by many martial arts including Hapkido.
 
Jigoro Kano also developed the belt ranking system for martial arts around the same time.  The gup (colored belt rank) and dan (black belt rank) system was originally a ranking and handicap system for the board game Go.  This system was later incorporated into the martial arts.  Jigoro Kano saw that Japanese competitive swimmers wore colored ribbons to denote rank and was inspired to utilize colored belts as a way of indicating gup and dan levels.  As the systems spread to other martial arts, different schools changed and added belt colors to suit their needs.