Only the smallest local bank or credit union would not have the ability to transfer money online via ACH for their customers. Pretty much everyone can login, go to the transfers tab, and enter an account/routing number to transfer money to (or give their account/routing number to another bank to transfer money in).

If you do not, then you should probably sign up for a free account at any of the multitude of online banks that do have the capabilities.

For example, at CIT Bank, which I easily opened a free online account, I have ACH limits of $250k outgoing and $500k incoming, PER DAY. All I had to do was enter my account #/routing # for my other bank accounts.