Beyond the simple freeze frame, there are essentially three methods of "stopping time," which may be mixed and matched as needed.
Multiple Camera Arrays: AKA "Bullet Time Rigs" are used to move the camera laterally in a single instant of time. They work by lining up a large number of identical cameras and taking a still or (less often) multiple frames in sync, which can then be sequenced in post to produce a moving image. This was made famous by its extensive use in The Matrix, of course, but was first seen in high-end car commercials. The disadvantage of this technique, aside from its on-set complexity, is that the shot has to move--either horizontally or vertically--because the cameras can't obstruct one-another's shots.
Photogrammetry: This is the technique of reconstructing a scene as a 3D model in post. Still photographs are mapped directly onto virtual geometry. The source photographs can come either from a "bullet time" rig, stills shot by the effects team, or even the original filmed footage. 900
The first extensive use of this technique was in Fight Club, to create impossible shots like the truck back through a car bomb, the "space exploration" shot flying through an office trash can, and even the surreal sex scene. The geometry (and here we begin to see the disadvantages) must be pieced together by specialized 3d tracking software with careful hinting by the effects artists, or generated by an on-set 3d mapping system--typically an expensive LiDAR system. Any camera move is possible, but fine details like hair and leaves are difficult to reconstruct, and even with the best systems a lot of man hours must typically be sunk into cleaning up the resulting 3D model and its textures.
Mimes: Sounds funny, but mimes are very highly trained movement specialists who can--among other things--hold still for a very long time! Made on a fairly modest budget, Clockstoppers used mimes extensively to save on special effects. Under the broader (and less tongue-in-cheek) category of "faking it," prop fabricators may be called on to model the splash of a tipped-over glass of milk (in silicon or another lookalike substance), pre-crumple and jack up the rear of a car to "freeze" it mid-collision, or anything else that can be realistically built.
As I mentioned, these techniques are often mixed and matched as needed. An actor might be hung on a wire, with glass breaking around her added in post. A bullet time rig might photograph the actors and foreground set, with the background created in pure photogrammetry. Special effects are about faking it just enough--and just long enough--to keep you engaged with the story. 900