I've carried a small mirror for a couple years. I got one of the signal mirrors in a trade, but since I doubt I'll ever need it for signalling, I don't carry it. I carry mine mainly for actually using as a mirror. There's times when being able to look behind things comes in handy.
My mirror... I have a buddy who has his own business creating and installing custom shower doors. He also installs mirrors. He'll give me a call every couple months when he has a mirror that's 4 feet wide and 8 feet long and needs help carrying it. (Or when he has a shower door that weights 150 pounds...

and he has to carry it up 3 flights of stairs and hold it up while putting the screws in the hinges)
I was in his shop one day after helping him and I remembered my "unbreakable" plastic mirror (which was in two pieces in my wallet) I asked him, next time he has a scrap piece, can he cut me a credit card-sized mirror? "Next time, hell", he says... he gets a piece of 1/4 inch out, traces some lines and starts cutting, ignoring my protests. The first two, he wasn't happy with, the third he liked. Took his belt sander and beveled the edges for me, then duck-taped the back, just in case it snapped.
I've had it in my back pocket, wrapped in a bandana ever since (going on 6-8 months now). I've squatted and put the heel of my boot on it and it's still perfect. Sat on tons of stuff and not even a scratch. I don't think I need to wrap it, but it gives me a perfect reason to carry a bandana. Plus, my buddy told me with a laugh :"You break that... let me know... I'll make you one of of 3/8 that's coated with acrylic!" He had a huge smile on his face as he told me that, almost daring me to break the one he gave me.