I don't even carry any of my airline cards unless I'm flying int'l. The only elite card I hold these days is AA, and I book all of my AA flights directly while logged in to my account, so my Goldness is shown right on the boarding pass. I have never needed to show the physical card to anyone.
I can't think of a really good reason I even carry it internationally...I just do. It's not like Gold by itself gets me into lounges. I guess I just have this fear that someday I'll get rerouted onto another One World carrier and then I'll need to flash it to get into an F check-in line or something.
I usually do carry the hotel cards just in case, but honestly I haven't pulled them out on any of my recent stays. I book directly at the hotel sites using my corporate code (if applicable) so my number/status is always on the reservation the first time.
The only card I always seem to have to use is my National Emerald Aisle card. It's a bit effing annoying...I have my confirmation number and driver's license, that should be all the data they need. (The printout actually has my EA number on there too!) But they always ask for the card, and the one time I did not have it, it was like a 10 minute ordeal to get out of the parking lot. The last time I rented, they wanted to see my EA card, my DL, and my credit card, and then - get this - keyed in the numbers by hand!! That data should already all be resident in the system: check my ID and contract number and be done with it!!