This entry will cover the ever popular desire to stabilize captured video. Having reviewed several avenues for doing this (even with dedicated video editing software), this method seems to be the best and provides the most control.
To get started, when first launching Blender switch to the Motion Tracking view.
The first step is to select a track point. This is simply done by holding [Ctrl] and [Right-Click] a point on the scene. Some things to consider when selecting a point. First find a point of good contrast that will not change between frames. This is the anchor for the scene.
In this case I chose the lamp sitting on the balcony.
Assuming you are on frame 1, if not move to frame 1 and readjust the track point. Now on the left panel window under the Track section, click the Play button identified below. This will build the track file for the point. If during play, your track view (shown above) goes blank and the process doesn't finish through the whole video, that means you lost track. Find a better track point.
If it completed processing the track the whole way through, find the 2D Stabilization panel (on the right) and enable it. Next hit the [+] button to add the track you just created.
If you play your video with [Alt + A], you won't see the effect of your stabilization yet, you need to find the Display section and click the Display Stabilization checkbox.
Now you should be able to view the effect of the stabilization on your video. You should be able to see an impact at this point, and possibly, even if the shake is resolved, rotation may still be a problem. Follow the same steps to add a new track point. In this case, select a point far from the original, but that is within the same perspective "distance" as the original.
In the window shown below, click the Rotation button and a second list should be available to add tracks. Now add the second track point there to account for rotation.
Finally note that in trying to keep the image stabilized, sometimes the edges of the frame are shown in the field of view. To fix this, check the Autoscale button shown below (note it is recommended when shooting footage that will be stabilized, to shoot wider than usual). This will scale the image to prevent outside frame regions from appearing in the field of view.
Also note in the image below that you can adjust the Influence of the location, rotation and scale effects.
Finally, to render your stabilized video you need to add this node setup in the compositor.