Via Mark Kleiman, it looks like some banks will deposit checks for you whether or not they're signed. Nice.
As it happens, my experience is that banks will also accept checks for deposit regardless of who they're made out to. I encourage the people I supervise to get their paychecks deposited into their bank accounts electronically. Still, several have not signed up for direct deposit. About a year and a half ago, two of those individuals - who also happen to share a first name - ended up with each others' checks. One of them noticed the mix-up before taking the check to the bank, but the other one had already deposited the wrong check.
Banks. Do. Not. Care.