Some good information and some mis-information in other answers. I have almost 9 years experience now working for one of the world's 4 largest sailcloth manufacturers. I manage manufacturing, R&D and QC for one of the factories of this company. read more
Additionally, and perhaps more importantly, there is one functional reason to have white sails: Dacron. The vast majority of cruising sailboats, as well as many dinghys and other racers, have sails made of woven polyester (PET) fibers. read more
One sail that is often not white is the spinnaker. This is the big balloon shaped sail that is flown from the front of the boat when sailing downwind. Spinnakers are usually made from brightly colored nylon panels and make a lovely sight on a breezy summer day. See the images in the source link for examples. read more