We were always told to accept as many forms of payment as possible.
Thats why we started offering a service in which a person pays by check over the web by entering their branch router and account number. A check printing agency would then send us the check to deposit.
Well, after a one year trial, I can conclude that it is a waste of time. Most people will pay by credit card over the web or by phone. Some people still prefer COD. COD works well if you call the customer to verify the order.
But paying by check electronically, is a waste of time. I got something like 12 cheques per 10,000 credit card orders. And two of them were bad.
So if some firm tells you that customers prefer to pay by cheque by the web, don't believe them. Its a lie.
Note: This post has nothing to do with paypal which is another processing system entirely. Please do not confuse the two.