Technique that seems to freeze everything in the world except the camera
It's called "Bullet Time" and was popularized by the movie The Matrix.  The effect is achieved by using many, many cameras to all shoot stills at the same time, and then effect of motion around the subject is achieved by animating across the different simultaneous images.

To make the effect more believable, the still camera has to really freeze the motion (because motion blur from a given camera-subject relationship contradicts the eye's expected motion blur that would come from motion tracing the path of the camera array that gives bullet time its distinctive look).  But perfectly still images usually make for fake-looking video, so to make it look more believable, motion vectors are derived from the sequence of stills and motion blur is then applied to the stills, completing the effect.

n.b.  Motion cameras that cam capture stills (from GoPro snapping away at 12fps to RED WEAPONs cranking out 96 fps at 6K resolution) can be used as a source for the stills.  This provides the opportunity for a two-dimensional bullet-time effect: in one dimension one can move through time as usual and in the other one can slide across space while freezing time.  This surf video from 2010 demonstrates the two-dimensional possibilities with a shed-load of GoPro cameras.