Legally, I think the answer is yes, you must. Practically, the answer is perhaps not (which is what Joe Taxpayer is aiming at, I think). Sorry for messing up you neat ethically-vs-legally distinction by adding a third category :)
The thing is, I'm pretty sure the line for legality in this case has to do with what you know - once you know you have the product, and didn't pay, you are responsible for making sure you do. Not paying for something, trying to avoid paying for something (without any agreement that you mustn't) is stealing. Once you know you weren't charged, once you know they messed up, it is your responsibility, legally, to make sure you pay what you owe.
Another part of it is, if (or when) you didn't know, you are not legally obligated to fix the mistake - which sounds kind of obvious at first, and then it doesn't since the fact of payment haven't changed at all - it is not that you didn't know about your obligation, as far as I know you were not obligated at that time. It was legal to leave it lie just a bit ago, and now it's not - because not paying "deliberately" versus "accidentally" are different legal situations.
Or to put it another way, if you walk out of a store without paying for something accidentally, it is a mistake not a crime. If you see it in you pocket, realize you didn't pay, and keep walking - that turns your mistake into theft. And different again is if you walk into a store, and see the cashier is not there, and do something like announce they can charge you for what you buy, leave your credit card on the counter while you grab stuff, and walk away with the stuff and your card. It's theft knowing that they couldn't have charged your card, because they weren't there to hear your "offer", even if you did "give them an opportunity to".
And going back to the beginning, I said legally yes, and practically, no. The "practically" is that if you didn't, there is probably not a good way to enforce that. The point at which this became a legal obligation is when you learned that you hadn't been charged, and decided to not take steps to meet your obligation (and in most cases, there would not be any witness to this decision). And the size of the purchase matters - it is less likely to be a problem for smaller errors than larger ones - as do the circumstances, since if you actually aren't in a good position to make amends (you were just passing through the area, or the seller was, or you can't get in contact with them for whatever reason, or it would cost more than the item is worth) it is more likely the cost would be written off by the seller.
There doesn't seem to be a good way to prove that you knew you hadn't been charged and kept silent, which is the precursor to holding you accountable for it (recall, you don't have a legal obligation when you didn't know). Unless you confess, or, well, unless they see this question, it doesn't seem practical to hold you accountable for your silence. Additionally, you are not likely to be held accountable by the seller, since they would likely view the error as their fault for not processing payment correctly, and so would be much less likely to go after you for not letting them know (especially since they wouldn't know, that you knew). So the "practically. maybe not" is that you could likely get away with keeping silent, even if it isn't legal.
And a brief note on ethics - it is of course ethically true that you must tell them, especially if it is for a larger sized purchase. They held up their side of the bargain, you really should hold up yours (or make a decent effort to do so). Or to put it another way, if the mistake was reversed - if, say, the seller didn't send the package, and maybe something came up so they couldn't, and you happened not to notice until your time to dispute the charge was almost up, would you be willing to let them not say anything so they could keep the money, instead of refunding or letting you know so that you could act? If it isn't right if it's happening to you, it isn't right for you to do to someone else.
