JET-SKI is a trademark of Kawasaki, and has become an all-purpose term for personal watercraft. Kawasaki began selling the original one-person stand-up Jet-Ski in 1973, thereby creating the personal watercraft business, which has since blossomed into a multi-million dollar industry with several major players.
Today, Kawasaki Jet-Ski products are sold in one, two, and three-person versions. The one-rider model (Currently the "Jet-Ski 750 SXi Pro" is primarily intended for racing, and features a 743CC two cylinder water cooled two-stroke engine topped with two Mikuni carburetors, providing a whopping 628 pounds of thrust - Quite a bit for a vehicle weighing 342 lbs and intended to carry only one rider, and only 83 inches in length. This is the product (or class of product) which comes most readily to mind when one hears "Jet-Ski". Two and three-seater models come with 1176 or 1071CC engines, and are intended for seated riders, though many people do stunts or tricks on these as well, and to cross choppy water it is necessary to stand, or be bounced around more than is probably good for you.
Kawasaki's main competitors in the personal watercraft arena include Bombardier, a multi-billion dollar company with interests in Aerospace and Transportation, and Yamaha, a metacoroporation which makes everything from motorcycles to sound cards.
References:
Website: Kawasaki Watercraft (http://www.kawasaki.com/watercraft/)