The only motorcycle ridden by any main characters on the TV show Breaking Bad, was ridden by Aaron Paul's character, Jesse Pinkman, and appeared in the first pilot episode and the fourth episode in the second season called Down. The motorcycle is a Kawasaki Concours ZG1000. The Kawasaki Concours is a sport touring motorcycle powered by a 4 stroke, inline 4 cylinder engine with shaft drive. The first generation Kawasaki Concours was manufactured from 1986 to 1993. In 1994 the Concours received major changes and pretty must stayed the same until 2006. In 2007 to the present the Concours motorcycle received another major makeover, which included increasing engine displacement to 1352cc.
The Kawasaki Concours ridden by Jesse Pinkman is a first generation model based on the wheel rim design. I wasn't able to pin point the exact year because you can't see detailed shots of the motorcycle and not many changes occurred from 1987 to 1993. I have read on other websites that the Kawasaki motorcycle that appeared in the Pilot episode was in fact a Kawasaki Ninja, and at some point between first and second season it was replaced with a Concours. I don't believe this is true based on the air vents on the motorcycle's fairing seen in the Pilot episode. The motorcycle used in season one and two is the same Kawasaki Concour model and I don't think a Kawasaki Ninja model was ever used on the show by Jesse Pinkman.
Jesse Pinkman's Kawasaki Concours ZG1000 from Breaking Bad, Pilot episode in season one
Jesse Pinkman's Kawasaki Concours ZG1000 from Breaking Bad, Down episode in season two
Jesse Pinkman's Kawasaki Concours ZG1000 from Breaking Bad, Down episode in season two
Kawasaki Concours first generation advertisement