My biggest problem is with sites that don't let me copy/paste into the password field. WTF!? Who's the PHB that came up with this policy? Despite this misguided nannying, I still use randomly generated 22 character alphanumeric passwords, even if I have to open up the window in Keepass and manually type them in. Most people aren't as paranoid and anal as me, however. Whoever you are, you're basically encouraging people to use weak passwords.
Ironic, as it seems to be banks that are most often guilty of this.