I do, when I pay my rent (my apt complex changes a fee for electronic payments,) and for any medical bills that I get in the mail (I'm not talking about copayments here - those go on my debit card.)
My normal monthly bills are all payed through electronic fund transfers, but if I'm not going to be making regular payments, I'd rather just write a check and mail it in.
Mark
Funny how things are inconsistent from business to business. My mobile home park doesn't take electronic payments at all, but my storage unit gives a 5% discount. Neither takes cash for good reason.