In RFID protocols, tags identify and authenticate themselves to readers. At Asiacrypt 2007, Vaudenay studied security and privacy models for these protocols. We extend this model to protocols which offer reader authentication to tags. Whenever corruption is allowed, we prove that secure protocols cannot protect privacy unless we assume tags have a temporary memory which vanishes by itself. Under this assumption, we study several protocols. We enrich a few basic protocols to get secure mutual authentication RFID protocols which achieve weak privacy based on pseudorandom functions only, narrow-destructive privacy based on random oracles, and narrow-strong and forward privacy based on public-key cryptography.