This is why I like Caffè Nero's loyalty cards. They are little pieces of cardstock with nine coffee cups printed on them. You get a stamp every time you order. Once all nine cups are stamped, redeem the card for a free coffee. There's no PII on the card and your name isn't going through an additional computer (on top of the standard 17 a day, per Cereal Killer).
More places should do this.