We saw a glimpse of this with Bullet Time in the Matrix movies and with Microsoft's Photosynth, but now a company called Replay Technologies has come up with the next evolution in what they call Free Dimensional Video.

Our technology works by capturing reality not as just a two-dimensional representation, but as a true three-dimensional scene, comprised of three-dimensional “pixels” that faithfully represent the fine details of the scene. This information is stored as a freeD™ database, which can then be tapped to produce (render) any desired viewing angle from the detailed information.
This enables a far superior way of capturing reality, which allows breaking free from the constraints of where a physical camera with a particular lens had been placed, allowing a freedom of viewing which has endless possibilities.

Essentially, you can choose any camera angle in post and the software can recreate it even if there was no camera shooting from that vantage point.

You can see an example of this in the tennis replays in the video below.

Amazing, and also refreshing, for once, to see a video technology debut in sports broadcast coverage instead of pornography.