Of course, we already have trains without drivers.... at the airports mostly.
In military flight, there are significant advantages to RPVs, a major factor being they can be significantly cheaper and smaller. A piloted aircraft on phot recon, for example, is as big and heavy as it is because of the pilot and all the safety systems around him from armour to ejector seats etc. RPVs are expendable and can risk enemy fire.
Dropping the crew from commercial flights, passenger or freight doesn't seem to provide the same level of advantages since the plane would still need to be the size it is to carry the same passengers or freight.
Technically it could be done, is it more or less risky? or is it going to be perceived as more risky? I suspect that the latter would be a transient fear.... witness the trains scenario... people are more accustomed to modern technology today than ever before.
The only question is would these be fully automated or remotely piloted? In either case I like AardvarkVW's thought about one pilot handling the landings of several different planes.... by the way, does it matter if the plane crashes because the pilot or the computer was victim of an instrument failure? The difference would be if, as Comcokid says, the pilot can make a difference in enough cases to justify his place.... if the money difference were enough then i guess that sooner or later like it or not that's what we'd get... pilotless planes. But is there enough financial advantage? Taking the pilot out would probably necessitate a significant increase in multiple redundnat systems based around different technologies (one fails the others shouldn't).
On the other hand, how many coputers would let their kids fly the plane (Russian pilot: crash wiped out all) or would have heart attacks, drink too much etc. Pilot error may often be a cop out but equally, pilot error also happens.
In the end, it probably will come down to cost.
JMW