I pay utility bills/rents online, via credit card, or via pre-approved debit.
For day to day purchases, I use a mix of credit card, cash and debit.
Debit, for those from the states, is a system whereby you swipe a card, enter a PIN number, and the money is instantly moved from your account to the account of the store.
I have used a cheque, relatively recently, to...
Pay rent
Buy a car
...
can't remember any other use of my chequebooks recently.