Speaking of banks with terrible websites, my credit union's login page features a checkbox for "Forgot my password", which is not only confusing in and of itself (" I need to enter my password to reset it?") but also is exactly where you'd expect the "Remember me?" checkbox to appear, meaning that any instinctual attempt for me to tell the site to remember who I am will instead result in me resetting my password.
I'm entirely convinced that banking website design guidelines are driven entirely by a seething hatred for the end-user.