We're with The National Bank, who have always been good. Their fee's aren't great, but you don't get charged any if you have a balance over $5000 like many other banks. They are a bit behind the times though, and still firmly believe in paperwork for everything. National was founded by Lloyds Bank, and has a pommy feel to it.

BNZ are more of a trendy, technology savvy bank. They always seem to be the first in with the new stuff, and their fees are comparable with the other major banks.

ANZ now own National Bank, so they are pretty much the same. The manager I spoke to in Auckland when opening our account said that ANZ was renowned for bad service, which is why they bought National Bank to help improve! They do seem to be on a service drive.

Our friends had an ASB account and had nothing but problems with them, but that could have just been that particular branch. They are also comparable with fees etc to the others.

Kiwibank is still a very young bank, with branches in most post offices. Their rates and fees are pretty good, with their savings account paying a whopping 7% interest (excluding withholding tax). No fees charged on balances over $4000.

Westpac have never really grabbed me. They seem to charge the highest fees and pay the lowest interest. Their credit card rates are also high. I haven't researched them for a few months now, so would be worth checking for yourself. Daisyspop seems happy with them!

TSB only have branches in Taranaki, Auckland, Wellington and Christchurch according to their website, so might make access a little tough!

All in all:

If you like trendy, technology and forward thinking - BNZ
If you prefer a more 'British' feeling traditional bank - The National Bank
If you want young, fresh and cheap, with good branch accessability - Kiwibank

Research them all though as rates and fees often change to meet competition.