If you use a filesystem that supports posix capabilities, an easy way to 
start wireshark as a normal user, while still providing it with all of the 
access permissions it requires, is by issuing the following command:
  $ setcap cap_net_raw,cap_net_admin=eip /usr/bin/dumpcap

One may also test if things are ok running this command as a normal user:

  $ dumpcap -L

You may also create a special group (wireshark) and include users allowed
to monitor networks in that group:

  # addgroup -S wireshark
  # manually add your username to /etc/group in the wireshark line
  # chgrp wireshark /usr/bin/dumpcap
  # chmod 750 /usr/bin/dumpcap
  # setcap cap_net_raw,cap_net_admin=eip /usr/bin/dumpcap

Other users not in the group wireshark can still open files with previously
saved monitorings and inspect them.