Just to piggyback on the other posts:
It depends on what kind of "look" you are going for. If you are going for a film look, then the 180 degree rule applies. So, 24 fps, 1/48 shutter, 30 fps, 1/60 shutter, (or as close as you can get it depending on the camera) 60fps, 1/120th, etc.
If you want more of a staccato look, and are not planning on manipulating speed in post, then a much faster shutter speed is necessary. For example, the entire storming the beach scene in Saving Private Ryan was shot at 24 fps and 1/96th shutter speed to create that look.
If you're looking for more motion blur - a "dreamy" look - then a shutter speed slower than 180 degree can be used.
I've also heard, and experimented with, plug-ins like Twixtor. If you have a higher shutter speed it seems to respond much better to slowing down footage.