Any router has the capability to do so, if it is enabled by the network administrator(doug and ePrix is half right. It won't log the history of website accessed, if it was disabled). It would record the incoming IP address of the site, and the IP of the local computer requesting the site. In addition, the computer itself can also record history of connections it made to what sites that are browsed and/or accessed. Fortunately, the administrator is able to clear the logs of Website access on the router. As for the locally stored, that cannot be cleared.
