Should you write your account number on the check when paying bills?

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Whenever I'm paying my electric bill or car insurance bill through the mail, I always try to remember to write my account number on the check. Partly, for the reason that I think they won't know which account to credit the money to otherwise. However, I think there should be some other way for companies to identify their customers, like a home address, telephone number etc. What do you think? Isn't all that customer information contained on the bill anyway? Why do they need an account number? If you sent a check for payment to a company and it didn't contain your account number do you think that they would be able to credit the money to the proper account? What would you do if you sent off a check to pay a bill and forgot to write your account number on the check? Would you call the company and tell them what you had done?