Here's some tools and libraries that look interesting for web development, mobile App development, etc.
To begin, 
Firefox and 
Chrome, of course, are the browsers of choice for a web developer.
Tools for Firefox
Firefox has tons of tools for web developers! Take special note of:
- Firebug,
- Console²,
- DOM Inspector,
- FoxGuide,
- HTML Validator,
- JSView,
- LiveReload,
- PageSpeed,
- Phoenix,
- SQLite Manager,
- Web Developer.
- ColorZilla 
If using Firebug, then also take special note of 
Acebug, 
FireRainbow.
 
 Tools for Chrome
 
Chrome is younger and has less tools, but many web developers prefer Chrome over Firefox.  And there are definitely tools:
- Google Chrome Developer Tools
- Web Developer 
- Firebug Lite
- Validity
- ColorZilla  
-  Color Generator
- Eye Dropper
JavaScript Validator
When programming in JavaScript, you must use 
JSLint to validate that the JavaScript you wrote conforms to modern recommended idioms.
You can run JSLint on the command line locally if the JSLint program is set up correctly based on the 
JSLint source files. But then a JavaScript interpreter outside of the browser is required, such as 
node.js, 
Rhino, or 
spidermonkey.  Another, more convenient, possibility is to use the 
jslint4java wrapper program.
 
Libraries
dust.js has been 
selected by LinkedIn recently as their 
templating engine to unify the way web pages designed in HTML and CSS gets filled with data generated by other server based programs written in various languages including Java, Grails, and JRuby.  It is free and open source (looks like MIT license)
PhoneGap is a free and open source (Apache License) library for writing 
cross-mobile-platform HTML5 app to access technologies native to the mobile platform (vs. programs being stuck in the browser).
For building 
gesture/touch-enabled UI for cross-mobile-platform Apps, there is 
jQuery Mobile, which is a very young project still, and is free and open source: dual licensed under MIT and GPL2.  There is also 
Sencha Touch, a more mature library that is free and open source, cross-licensed under GPL3, a modified GPL3, a free (as in beer) commercial software license, 
and a paid commercial OEM license.
You might also need a library to add 
MVC or MVVM structure to your App.  For that, consider 
Backbone.js (MVC) or 
Knockout.js (MVVM).
For everything else, there's 
jQuery.
See also:
-  Building Large-Scale jQuery Applications
- Tools For jQuery Application Architecture – The Printable Chart