Good question.
This has become an important topic as people want their footage to look less like a video camcorder and more like a cinema camera. Shallow depth of field and control of the aperture is a big part of it, but so is control of the shutter.
In general you want to keep shutter speed fixed so your footage has the same amount of motion blur. Think of it has visual rhythm or beat. If you change the shutter speed from scene to scene, the amount of motion blur will change and ruin the steady visual rhythm.
There is also a general rule for specific shutter speed settings to create natural looking motion blur. You want your shutter speed to be approximately double the recording frame rate. So if you record at 24p, shutter should be close to 48 (50 on the Canon) 30p, shutter should be 60.
Some knowingly break these rules to create a visual affect. Think Saving Private Ryan the beach scene. You can also break the rule if there is very little motion in the scene.
Below is a link showing the affects of shutter on motion blur. High shutter shows more detail, but is not how your eyes would see it live. Your eyes would see more motion blur.
Shutter Speed Test - "Tarantella" on Vimeo