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Stabilizing a space craft or rocket with a spin is a rather easy way of keeping its trajectory straight while it is under powered flight. You do not need to gimbal rocket engines and you can work without thrusters or active control surfaces.
A typical example in terms of rockets are sounding rockets. Within the first few seconds of the launch, they are spun up to a few rotations per second (by fixed control surfaces) and therefore keep their pre-arrange trajectory while under powered flight. At motor burnout, you can de-spin them with yo-yos, if you like. There is no better way to show this than with a video: http://www.youtube.com/watch?v=5nlVcRtBTLQ (yo-yos are used at 1:50).
Some space probes are stabilized in a similar fashion. The following video is a computer animation of the MERs' flights to Mars: http://www.youtube.com/watch?v=XRCIzZHpFtY The several stages of the Delta II itself are stabilized with gimbaling rocket engines and gyros. However, at 1:18, you can see how the final 'stage' for insertion on a trajectory towards Mars is spun up before it is ignited. Once the engine has stopped at 1:37, you can see the yo-yos.
The nice aspect about spin stabilization is, that it allows rather simple designs. You can save a lot of moving parts, weight and complexity. If you do not need to change your orientation while engines are running, it is a perfect concept.