Loyalty systems provide an interesting possibility for vendors in customer relationship management. This holds for both real world and online vendors. Beside potential benefits of loyalty systems, customers may fear an invasion of privacy, and thus often refuse to participate in such programs. In this paper, we present two variants of a privacy-friendly loyalty system to be used by online vendors for issuing loyalty points. The systems prevent vendors from exploiting data for the creation of customer profiles by providing unconditional unlinkability of loyalty points with regard to purchases. We propose a simple token-based approach and a counter-based approach which is much more efficient while preserving the privacy and security properties. Furthermore, the counter-based loyalty system prevents pooling of loyalty points issued to distinct customers.