The technique is called "bullet time", and as stated by @DrMayhem, involves lots of camera. I seem to recall that The Matrix VisFX team had enough cameras to do 60 frames per second.
That being said, check out Vincent Gallo's "Buffalo 66" and look for some articles on line. I think American Cinematographer did a piece on it around the time it was released. On a limited budget with a SINGLE camera, the closing scene is a pretty convincing bullet time sequence. He held REALLY still while the camera rolled a few seconds, cut, moved about 5 degrees along an arc, rolled for a few more seconds, cut, moved, rolled...until they'd travelled along the arc as far as they needed to. Circular dolly track makes this a LOT easier, but I'm sure a creative mind can figure out a way to simulate that... :)
Any jitters were smoothed out in post by morphing one frame to another...they probably had about 100 - 200 frames of each camera position from which to choose. A pain in post, but single camera bullet time.
I've been muddling a DIY circular track in my head; A digital SLR on time lapse mode with the actor holding still is the next thing I want to try. I can get a solid 8fps; animate the other 16fps by interpolating from existing frames, e voila.
There's a lot of DIY Bullet-Time stuff on the web as well.
http://www.instructables.com/id/How-to-Enter-the-Ghetto-Matrix-DIY-Bullet-Time/ is one of my faves, though a little more complex than a single camera.