I don't know about banned, but should they be at least discouraged from? I personally find the pun an amusing template for creativity. The pun is at the heart of life and progressive expression, anything that has ever been had a metaphor to base itself upon. If you look at the arts in particular you can witness the isomorphing of music and film changing with the time, but always reflecting something from the past whether it be new or archaic. Some people find them annoying and gassy. Sometimes their humour is based around the fact that the pun is cheesy, predictable, lame, or downright copycat, other times it can be very creative and thoughtworthhy. At the very least I think it should never be censored, no matter how repetitive or competitive it may seem.
No banning puns! Some of the best punsters (is that even a word?) are on here and their imagination and creative word play is fun to read. If anything we should encourage puns.