+Colin Bowen's tip (https://plus.google.com/+ColinBowen/posts/7kdeWtSBpwE) about having his Tesco clubcard scanned in his shopping list just reminded me:
I use an app called Stocard for all sorts of loyalty and membership cards. It's UK optimised, but would presumably work elsewhere - you just wouldn't get the benefit of their library of logos for your cards. (I have added some that aren't in their library, and in some cases photographed the card to get a quickly recognised logo.)

You can add a card by picking one from their library (for the logo/description) and then either scan your card with the phone's camera, or enter your details manually. Even for the ones you enter manually, it produces a bar code for the card. For reward cards that it recognises, you can associate it with your login to see how many points you've earned (although I haven't tried that). You can add photos of the front and rear of your cards if you want to. Sometimes there's useful information on them!

I have various shops' loyalty cards, my blood donor card, assorted club membership cards, breakdown recovery membership, etc. stored in it, and all backed up to Google, so switching devices doesn't lose them all.

There are a whole load of loyalty/discount cards that I only ever use once in a blue moon, and carrying them all in a wallet would be a real PITA. This way, I don't need to.

If you want it to, it can remind you of offers when you're near the stores that the cards apply to (although I switch that off, as it can get a bit intrusive).

Apparently, it now also supports Passbook Passes, although I don't have any to try it with.

Android: https://play.google.com/store/apps/details?id=de.stocard.stocard
iOS: https://itunes.apple.com/gb/app/stocard-loyalty-cards-wallet/id444578884?mt=8
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