Firebug Net Panel Logs
Edit: Just thought I'd edit this since all the answers on this page are now out of date... As of version 1.5, Firebug lets you retain your net panel activities between page loads by selecting the
Persist option (at the top left, next to
Not that I'm aware of out of the box... If you're just trying to record the header request/response info (as opposed to the actual content & timings), you could try Live HTTP Headers. Not as pretty, but I still find it useful in certain debugging scenarios.
You may use HttpFox. This does exactly what you want, and also what I wanted. That's why I recommend it.
Check out this post that explains how to persist Net panel entries across page reloads. http://www.softwareishard.com/blog/firebug/firebug-tip-observe-page-redirects/