Just Procrastinating has an example of why I will never do on-line banking of any kind. Due to a mistake - maybe even his own - his $45 cellphone bill turned into a $4500 deduction from his account.
If he had written a check this wouldn't have happened. If he had used a credit card payment he could dispute the charge.
This is the reason I never, ever give vendors of any kind access to accounts with real money - even PayPal only has access to a credit card. A mistake of any kind results in the vendor having the money. And they return it to you at their leisure, if at all.
Someone else I know had their cable bill automatically deducted from their checking account. Someone managed to hack into my friend's cable account and get their cable charges deducted from his checking account as well. More than a year later my friend still doesn't have his money back.
So if I pay electronically at all, it is only with CREDIT cards (never debit), where I can dispute the charge. In fact, I don't carry a debit card at all since that is another way to give vendors access to my money. Credit card companies (at least mine) automatically reverse any charge I dispute for 30 days while it is worked out. So this policy gives me the power to tell vendors to screw themselves and is an extra level of protection against mistakes. Of course I pay off my cards each month, so I am not paying astronomical interest rates for the convenience.
But the vast majority of my banking is by check and stamp, and I will probably be one of the few people in 30 years still using the "old method".