Regardless of what language you use to build your web applications, there are a couple common tenants and tools that I feel are useful.
First, I strongly believe in the idea of permanent URLs. I agree with pretty much everything this W3C article says. All your URLs should be permanent, obvious, and technology agnostic. While this isn't strictly a tool, I think it is important for everyone building public websites to at least consider and realize the trade-offs they are making by breaking these guidelines.
Firefox. Yes, you should also test in IE, Safari, etc. but Firefox is a great tool for your primary development. It provides great information out of the box. Plus, there is a great set of plugins that are very useful:
Web Developer - It provides great introspection information, and on the fly CSS editing. The list goes on. This is a must have.
YSlow - A Yahoo add on to FireBug that provides insight on how to improve your page load time.
Live HTTP Headers - Watch the HTTP Header information exchanged between the browser and web server.
Extended Statusbar - Displays information about how fast a page loads and how big it is. I've found this one interesting but not critically useful. Anyone have a better suggestion?
ColorZilla - Allows you to grab color information from images/pages.
Does anyone have any other must have tools?