Is there a official classification for turbulence?

In addition to Michael's answer, there is another classification of turbulence:

• Anticipated turbulence: This is the good type. The captain will know about the turbulence in advance and will try his best to avoid it. In case the turbulence is not avoidable then the captain will notify the cabin crew. The cabin crew will announce that to the passengers and prepare the cabin for the worst. In this kind of turbulence things are always fine because people and the cabin are prepared for the turbulence.. seat belts are buckled up and cabin items are secured. One more thing, this kind of turbulence most likely to be safe because the captain would not risk entering the turbulent area unless the airplane can handle it safely.

• Unanticipated turbulence: This is the evil type. The forecast and the airplane's radar will show clear weather. The cockpit crew, cabin crew and passengers are not notified in advance and the cabin items are most likely to be loose (carts, trays...etc). This type is really dangerous and most likely to be severe and causes injuries specially to the people who are standing and due to flying unsecured items. That's why in the seat belt off announcement the announcer will say something like (The seat belt sign has been turned off, for your safety keep your belt fastened at all times unless you need to move). So it is highly advised to keep your seat belt fastened at all times unless you are going to toilet or so.