Don't bother trying to do any anonymous surfing in the library in Naperville, IL after the beginning of the summer. As a matter of fact, don't borrow your friend's library card either, because it won't work. Starting in June, the library will be replacing their library card+PIN security system for access to the Internet with fingerprint readers.
Although the library maintains (according to this article in the Chicago Tribune) that their system cannot be cross- referenced with the FBI's fingerprint listings, it certainly doesn't appear to be a step forward for access to information.
Now, I can see that they may want some way to make sure that the kiddies don't get online to see things that they shouldn't see, but to me, the solution to that is selective filtering on computers that are in the sections of the library that are open to children. If you can have sections for adult-oriented books, then you can do the same for the internet--filtered for the kids, unfiltered for the adults (or at least less filtered).
However, the reason that they are taking this action is a bit more disturbing than that. It appears that two events caused the investigation into more security: the introduction of parental controls for children (on request of the parents), and the perceived need to cut down on people accessing the library systems without the library knowing who they are.
The latter stems from a case last year when the library received a subpoena to identify somebody who was seated at a computer in their facility at a particular time. Fair enough, they had a subpoena in this case, and evidence shows they denied a request from the police without the subpoena, but with the information stored away there is nothing preventing the information getting out but the good will of the library and whatever policies and laws may exist as of the day the request is made. Somehow, I don't think they'll be deleting the information very quickly and the audit trail isn't quite going to be what HIPPA requires.
All things considered, if you want to access the internet anonymously, find yourself a coin-operated kiosk (if you can find one) or buy a WiFi card and use it in your laptop (instead of the built-in WiFi, since that's linked to the manufacturer and serial number of your laptop) and use a free hotspot someplace.
Paranoid? Nah... I surf from home and on paid services, so I'm pretty sure they can watch me if they want to.