QR code expires?

Static QR codes, like the ones InDesign create, do not expire, as long as the information they contain is still correct. e.g. if it's a QR code that directs someone to a website, if the URL has changed in any way after the code was created, the code would no longer work and would need to be changed. 

As far as business card vCard QR codes, the ones InDesign created used to be at v2.1 which caused some issues with some smart phones that now require v3 and up, but that has been upgraded in the current version.

Free online Static codes should be fine as well, but it depends on how reputable they are.

What you are referring to are most likely Dynamic QR codes, which can be much simpler, but are quite different in that they are not hard-coded like Static ones, and are usually a simple redirect to a website/service which then sends it on to the actual destination that's stored in their server; the benefit being one can update the information at any time without having to change the actual QR code so you don't have to reprint business cards, say. Again, if these are obtained from reputable sources/services they should not expire even if that service shuts down (which happens more than you think), but you won't be able to update them any longer so would eventually become useless. Many of the "free" sites may also use a redirect which might direct traffic/info to be used for other purposes, like ad serving/tracking, etc, and probably cannot function if the server end is discontinued for any reason, like if the "free" website shuts down or is abandoned.

So it's buyer beware. "free" does have a cost to it in the end.