I have been using billpay through my credit union and automatic deduction for utilities since before I got married (7+ years ago). I have a checking account, but haven't had a checkbook for over a year, that's why I have asked some brothers to accept online credit card payments (I won't mention any companies) for cigars they are selling, because I really don't have any checks and don't have a desire to go get any.
My paychecks are direct deposited into my checking account. My credit union automatically deducts a set amount of money each payday into my savings and some into each of my daughters savings account. Then all my bills automatically come out either via billpay or auto deduction in time for their due dates. It's nice not having to worry about paying bills. I know I have them, but they are always taken care of. I log into my checking account a couple times a month to make sure things are paid and to check on my account balance, but this way, it's one less thing to worry about. I haven't mailed a bill out for more years than I can remember.
I just recently pulled my free credit report through all three agencies. I have never had a late payment on anything, so I know the bill pay system works well, and has for over 7 years.
I agree though that you should really watch everything the first month just to make sure it goes smoothly.