What if I deposit a check into a Bank of America ATM but forget to endorse it with my signature on the back of the check?
If a bank employee catches it then typically they would call you and ask you to come in to sign the check. If they can't get a hold of you they would probably mail it back to you. There is a chance that they won't catch in which case it would just be deposited into your account like any other check.
You do not have to endorse a check at the bank you have an account with. By leaving the back of the check blank, and thus failing to endorse it, you automatically endorse the check with a restricted endorsement (similar to "For Deposit Only").
As such, the teller wouldn't have to call you back to the window as alluded to in stoj's answer.
For clarification see Restrictive Indorsement in the Uniform Commercial Code (UCC) § 3-206 Subsection C.
The reasoning behind endorsing a check is to restrict what other people can do with the check. If you're the named Payee on the check, then of course you can deposit it without an endorsement. If you endorse it as "for deposit only", then someone else who gets ahold of it can't deposit it into their own account (because you're the payee, not them). But if you leave it blank, then they can fake your endorsement (e.g., "payable to Joe Blow") and try to cash it or something.
It may clear, or they (either bank) may call you. I'm POA on my mother-in-law's account. When she wrote a check and forgot top sign it, it made it through the first bank, but the bank the check was written from called me. I was able to fax them an authorization to clear the check, and all was well.
The banks in the U.S., when I worked for one, had a stamp that says "Deposit Only To the Within Named Payee" for deposits only if the name on the front of the check matches to the name on the account it's going to....it's logical considering it's being deposited to the person the check is made out to. Funds will most likely not be available for a few days however, under these circumstances.
Almost all checks are processed electronically nowadays. Thus, signatures probably don't matter much unless you use the teller and you want cash instead of a deposit. However, I would still think that they spot check some checks and if you don't sign then as luck would have it, they'll pick your check to spot check. This may delay clearing the funds for your use until the matter is taken care of.