I use the CardStar App for my rewards cards – I detest carrying extra stuff around, not even a purse if I can help it.
There are specific bar code scanners that can read the phone screen – at Starbucks and CVS, for example. Other stores it seems to be the hand-held scanners that have better success than the ones built in to the checkout counter… which is the case at PetCo and Stop & Shop.
I also have the impression that it has to be an App for this purpose – not just a PDF of the bar code – perhaps they render the codes differently via the apps to make them more readable. I seem to recall one emailed coupon where you could choose either a printable version or a mobile version of the coupon – might have been Bed, Bath & Beyond or Staples – the retailers are also concerned about making sure certain coupons can only be used once, so the mobile option presents that challenge, too.
It seems that increasingly more shops are getting mobile functionality. Check the websites of the stores you frequent to find out whether they have an app or partner with any apps for this purpose.