Collaborative tagging has been quickly gaining ground because of its ability to recruit the activity of web users into effectively organizing and sharing vast amounts of information. Here we collect data from a popular system and investigate the statistical properties of tag co-occurrence. We introduce a stochastic model of user behavior embodying two main aspects of collaborative tagging: (i) a frequency-bias mechanism related to the idea that users are exposed to each other's tagging activity; (ii) a notion of memory - or aging of resources - in the form of a heavy-tailed access to the past state of the system. Remarkably, our simple modeling is able to account quantitatively for the observed experimental features, with a surprisingly high accuracy. This points in the direction of a universal behavior of users, who - despite the complexity of their own cognitive processes and the uncoordinated and selfish nature of their tagging activity - appear to follow simple activity patterns.