Wireshark is the world's foremost
network protocol analyzer, and is the
de facto (and often de jure) standard
across many industries and educational
institutions.
There is a bit of a learning curve but it is far and away the best tool available.
Wireshark if you want to see everything going on in the network.
Fiddler if you want to just monitor HTTP/s traffic.
Live HTTP Headers if you're in Firefox and want a quick plugin just to see the headers.
Also FireBug can get you that information too and provides a nice interface when your working on a single page during development. I've used it to monitor AJAX transactions.
Fiddler is great when you are only interested in the http(s) side of the communications. It is also very useful when you are trying to inspect inside a https stream.
I like TcpCatcher because it is very simple to use and has a modern interface. It is provided as a jar file, you just download it and run it (no installation process). Also, it comes with a very useful "on the fly" packets modification features (debug mode).