My online checking account at ING Direct offers free online bill paying, and they also will send a paper check (at no charge, they even pay the 41 cent postage) to anyone you don't want to or are unable to send an online payment to.
I don't know why people are so skittish about giving out account numbers. Every time you pay by check, your check has the name of your bank, and your account number on it, as well as the routing number, all the information you need to send an online payment. So what is the worry about privacy? If you're worried about that, stop writing checks.
The ING Direct checking account also pays 3.63% interest with no fees and no minimums, and is FDIC insured.
What's not to like? ING DIRECT - Save Your Money!
and ask about their Electric Orange checking account. (You can also open an Orange savings account, that pays 4.5% interest that also has no minimums and no fees, and money from it can be transferred to your Electric Orange checking account as well as two others at any time, free of fees. Also FDIC insured. (They do not link to brokerage accounts, however.)