We share a bank account; if the check is made out to me personally, can I have my other half run it to the ATM while I'm at work? Also, is it legal to do so?
As you are depositing the check, there's something simple that you can do that will make this work very easily. Sign the check, and write the works "For Deposit only
<BANK> Account #
<ACCOUNT NUMBER> (Replacing the
<ACCOUNT NUMBER>, of course), then you can use any means to get the check to the appropriate location, so long as you were the person to sign the check. It's perfectly legal to do this, or even to send a friend. My bank actually allows us to mail the checks, making it be a stranger that I don't even know bringing the check to the bank.
However, the question of if your SO could sign the check in your absence, well, it might be doable, especially if you are depositing the check into a joint account, but I wouldn't do it on a regular basis. If there's an emergency, it could be worth a shot, but aside from that... I would not try that unless you have some sort of a legal contract, either being married or some kind of power of attorney or similar document.
The bank will accept a deposit into the account regardless of who tries to do it. My wife can intercept checks to me and deposit even with no signature.
As I've answered in similar questions, banks may have their own rules, stricter or more lenient than the law suggests. For example, one teller cashes my wife's check, but other one asks me for ID.