Understanding the Web Browser Threat is an essay that details web users and the browsers they use. The primary focus is on how current one’s browser version is, as opposed to evaluating one browser against others.
It is too little understood how dangerous using an older version of a browser can be for a user. If you are using a current version of a browser, any of the main varieties will do, you will be much, much safer than using an older or unpatched version.
Check not only your own computers for this, but also your public access terminals. Older browsers put all of your patrons at greater risk, as well as your library’s network.
My own recommendation: Firefox (currently at version 3.01). Not only has Firefox been quick to fix security issues, it has automatic updating built into the program. It also works on any platform (as well as from a Flash Drive), so it is about as universal a program as you willl likely find.
thanks to Jessamyn for the link!