Some users of the jutsu are Kakashi, Gai, Genma, Kabuto, etc. It can often be seen when Anbu members are dismissed.
The most common one I know of and I think you are talking about is the Body Flicker Technique (also known as Teleportation Jutsu, or Shunshin no Jutsu).
The Body Flicker Technique is a high-speed movement technique, allowing a ninja to move short to long distances at an almost untraceable speed.*
To an observer, it appears as if the user has teleported. A puff of smoke is occasionally used to disguise the user's movements. It is accomplished by using chakra to temporarily vitalise the body and move at extreme speeds. The amount of chakra required depends on the overall distance and elevation between the user and the intended destination.
It could also be a shadow clone.