ASB's Streamline account has a $0.00 monthly fee and $0.00 for transactions (as long as any ATM withdrawals are done from ASB ATM's, and you don't do any manual transactions at a branch)
From http://asb.co.nz/section367.asp?
"We thought $0.00 sounded like a great amount for a fee, so that's what we've made the transaction fee on all of our electronic transactions. You'll get the monthly base fee waived if you choose to monitor your accounts online instead of receiving paper statements."
I was with KiwiBank for a while, wanting to be patriotic and all.....but ASB (owned by the Aussies) won me over with the $0 monthly fee and $0 transaction fees.