ACH is obviously replacing paper checks for many applications, such as direct debit for recurring payments such as insurance, car payments, mortgages and of course, porn memberships. ;-)
There are still many people who do not have online banking, so online bill payment is not a viable option for them.
Even when it is, if the receiving party is not set up to receive an ACH, guess what happens.... the bank prints a bank draft (paper check) and deposits it.
People who use credit cards often pay their monthly bill by writing a check. Same with Cable bills, phone bills, etc.
Paper checks are ingrained in American society and the use is still on the rise. 65 billion checks will be written in the US this year.
http://mitsloan.mit.edu/newsroom/2002-gupta.php
In October of this year, Check21 (the imaging of checks) will be the next major change to how paper checks are processed.