The only reasonable option is "Punk Free Gaming". As others have pointed out, eGO doesn't exist to ban; rather, it exists to provide a clean fun place to play. So, why would we detract from our mission and pigeon hole ourselves by putting ban in our slogan?
Adopting a slogan that contains the word ban validates the ignorant players' belief that we are nothing but a ban-happy bunch of children with admin power.
Let's imagine a conversation between a couple of reasonably-intelligent people who just don't understand our rules.
"Can you believe that they banned me?"
"Well, they do say 'punk-free gaming', and you were being a punk."
"I still don't agree with it."
"Can you believe that they banned me?"
"Well, they do say 'dropping the ban hammer'. Maybe they just needed to ban someone."
"That's crap. I'll never play there again."
"Neither will I."
The players who don't follow our rules are the only ones that should fear the "ban hammer". Regular players shouldn't even have to think about it until they are glad that an active admin banned a jerk from the server.