You might want to delete the internet access logs from your computer occasionally (or regularly, depending on your privacy concerns). Your operating system's firewall log and your browser's "history" are probably the most common examples of internet access logs. In fact, if you have no use for a record of the sites you have visited, you might as well disable your browser history entirely. And, of course, make sure to delete your browser history when you're done using a public computer.
The access logs on your router or wireless access point will be impossible to delete unless you have administrative access. You may want to change your MAC address as an anonymity measure and use a proxy service like Tor to hide your internet activities.
