I spend a lot of time troubleshooting web applications. My Swiss army tool of choice for all network related issues is WireShark but it falls short when it comes to analyzing SSL encrypted traffic.
FireFox takes forever to load compared to IE7 but its wide range of add-ons can be a life saver at times for developers. I am a heavy user of:
User Agent Switcher which quickly lets me change the user agent of the browser
SwitchProxy lets you quickly swap between proxies. Proxy configuration scripts are great if you always use the same proxies but I frequently have to force a specific proxy to test different web application behaviors.
LiveHTTPHeaders plugs into FireFox ...