The short answer is that it depends.

Grounding a screened (shielded) cable at both ends could, in some circumstances, cause ground loops (hum). Also, when you consider fault conditions, you might be trying to force a Brazillion amps down the shield; this could smoke an airplane out of the sky. Sometimes the far end of the cable doesn't really have a good (RF) ground anyway so there's nothing to ground to anyway.

There are plenty of arguments on the other side too.

Standby for additional replies.

From what I've seen, in general it is better to try attaching shield at both ends.  The logic I've seen is to lift the noisey end to decouple it.

Connecting at one end only creates more of a Faraday cage, where you want no current flow.  But if you want a magnetic shield for higher frequencies, current flow will counteract the E-field.  So, the way I look at it, if 60Hz is your noise then attach at one end.  If switching noise is bad for you, then attach at both ends.  You may have to use a small resistor to limit current flow.  I'm out to try attaching the overall shield at one only, and the inner conductor data shields at both ends.

One way to get good shielding, without currents flowing in the screen and maintaining controlled impedance, is to use triaxial cable (and connectors of course). The inner coaxial gives you the 50 (or 75) ohms as required and the isolated extra screen gives an overall shield which can be grounded whichever way you want: Faraday - one end, or both ends, if you need to.

I recall reading something in Henry Ott's book that the answer  depends on the "type" of noise you are concerned about.  

I can't recall the specifics, but I think it had something to do with whether the coupling was from an electric field or a magnetic field, but I may be mistaken here.