There was no such thing as banks or checking accounts back in the times in which the Torah was written. Furthermore, things like online banking probably could only be imagined by Adonai himself.
But the Torah does speak to some issues in banking and the handling of money; it condemns charing unreasonable fees and interest, calling such things a sin known as “usury.” Usury is just that – charging people unreasonable fees and interest for the use of the money you lend them.
While times have changed how such usury practices are defined, there are plenty of banks that I think might drift afoul of this ancient sin. For example, I have a married couple who are friends of my wife and me who overdrew their account by a few bucks and within three weeks or so, lost an entire paycheck to the quickly-accumulating debt and still owed over $1,000.
That’s certainly an example of usury.
That’s why it’s good to be careful in selecting a bank, and while online banking might not be Torah-endorsed, it’s certainly a good idea to take advantage of all the options and features an online bank like WaMu has to offer. While there are many good banks still around, a few I won’t name here are getting very impersonal and heartless.