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Many different schemes
Payback is the most well known  - For example for DM, kaufhof, karstadt aral (bp) are all in a partnership.

Every 1€ spent is 1 point.
Payout Every 100 points is 1€. So every 100€ Spent gives 1€ discount.

The reason why the shops participate is that they can all share in learning about your personal buying behaviour :

1) how much do you spent per month on groceries, fill your car, ..., where you purchase.
2) how much a demographic spends on groceries.
3) trends - what type of food a demographic spends (bio, tolerance to flavourants,...,
4) more targeted ads that on facebook, amazon, ebay, google searches, and flyers to your home.
5) price sensitivity, how long you shop around, so that they don't have to give you too much discounts.
6) sudden behaviour changes in your buying pattern ( usually a sign of new job, pregnant, switching partners, new friends)

For 1/100 cent you sell your soul.

I dont have it myself (thinking now to get it) but a friend has got mamy things for free from Rewe and Real such as knifes, frying pans etc.

I have never bothered with payback cards. It is correct that it results in the companies collecting marketing data. But then paying with plastic would do the same thing but I don't see people switching to cash because of this. Some businesses give out a little booklet that one fills with stickers - redeemable for things like knives and frying pans etc. as Epicuriousannie mentioned. This is reward for being a repeat customer without any tracking involved. I never bothered because I rarely want what they have to offer.

But Penny supermarket just introduced a new version. One gets a booklet with a purchase over 20 Euros. One gets a stamp in it for each additional such purchase until one has done it 3 more time. Then one gets a 4 Euro rebate, spendable on whatever you purchase. Since I regularly shop at Penny for such amounts I see no reason not to participate - no tracking of my specific purchases and no unwanted junk.

Seems that the "Stempelkarte" strategy from Penny that I mentioned above has been disconinued. Was good while it lasted... They still have the system where one collects points for free gifts like small stuffed animals and other junk...