Honestly, I haven’t given much thought to boarding passes. When I have a printed one, I typically hang on to it and throw it away once I reach my destination, assuming that once the flight has been completed, it has no value. (I am crazy about not losing it before a flight, out of what is probably an irrational fear of someone else boarding the plane in my place, but hey, it’s my fear.)
Given all of the information about me that is available in the text, let alone the barcode, I should probably hang on to all of them until I get home and shred them though, instead of tossing them at the hotel. Or, always just use electronic ones, which stores them on my phone, but really,aren’t we all taking precautions to protect all of the other data that’s on our phones anyway?