jamesrobert: Been using direct debit (rates, telco, power, Sky) for ever (30-plus years). Never had a problem. Cheques? Different story.
I do everything online with online banking. Get all my bills via email. Payees are all saved at the bank site so it's easy, automatic payment ( not to be confused with direct debit) set up for rates fortnightly after pay day. We pay everybody that way... tradies, our mechanic, IRD, ISP etc. Very convenient, very easy to track. I haven't had a chequebook since Lord knows when but some people still use them.
You can pay your insurance with online banking. Or via credit card. You can even pay your traffic ticket, car licenses etc. online. Mortgages I don't know.