Err, 48 if you count the whole works:

perl -e'@l=<>;print while($_=splice@l,rand@l,1)' </CODE>

Update:
Best beat myself before someone else does. As often occurs, map inspires and produces useful results. 46 characters:

perl -e'map{splice@l,rand@l+1,0,$_}<>;print@l'

Or, if you really want to get down to brass tacks, 45 characters:

perl -e'splice@l,rand@l+1,0,$_ for<>;print@l'

Note that the '+1' can be eliminated if there is a blank line at the start of the file.

Update 2.0
It occured to me to break sort and make it act all screwy, which sure jumbles up the text a fair bit, for all intents appearing totally random. 31 characters:

perl -e'print sort{4-rand 9}<>'