You can use a proxy server, such as:
http://proxify.com/
If you're at a University, you probably have proxy service available there for free.
As far as the Mac using Safari part, you can set Safari to spoof another browser from the debug menu. Doing so may possibly have deleterious effects on your browsing experience, so you have to decide whether being anonymous is preferable or having websites *work* is preferable.
Ultimately, of course, if you use the web for the commission of a crime, using a proxy server is unlikely to assist you, though.
I'm pretty sure they keep records, which they would be forced to disclose by a court if the circumstances justified it.
*shrug*
In the end, to me, it's like a phone call. Why should you expect the right to call someone without them knowing it's you who's calling? In the same way, why do you expect to be able to be anonymous when visiting websites? If you were a hacker (not that you are ... if you were, you'd already know all of this) and you were visiting my site, I'd want a way to track your basic net identity.