Description of problem:

$ ionice -c3 :
ioprio_set: Operation not permitted
$ 

Version-Release number of selected component (if applicable):

These don't work:

kernel-2.6.24.4-84.fc8
kernel-2.6.18-53.1.13.el5

2.6.25 in Fedora works fine.

Additional info:

Actually this is documented in ionice(1) manual:

       Idle.   A  program running with idle io priority will only get disk time
when no other program has asked for disk io for a defined grace period. The
impact of
       idle io processes on normal system activity should be zero. This
scheduling class does not take a priority argument. This scheduling class  is 
not  permitted
       for an ordinary (i.e., non-root) user.

Adding Karel to Cc:, since he maintains package that contains this manual page,
and IIRC he's also upstream for it, so he should probably adjust the manual page
to reflect the fact that at least in 2.6.25 the situation is different.