Annotated List of 15 "must-have" web developer tools compiled by designer Andrew Sellick. The list includes some of the usual suspects, like Dreamweaver and Photoshop, but also some lesser-known tools, such as Feng Gui and Fiddler. Many of the tools are free, and the comments section expands on the list with additional free and open-source tools. Here's the list:

1. Adobe Photoshop $649, also available as part of Adobe Creative Suite package
2. GIMP: photo manipulation software. alternative to PS. free
3. Adobe Dreamweaver $399, also available as part of Adobe Creative Suite package
4. Color Cop: captures colors on your screen (Win). free (donation requested)
5. Firefox web developer toolbar: adds web developer tools to Firefox. free
6. Internet Explorer Toolbar: for creating, understanding and troubleshooting websites. free
7. Firebug: Firefox extension for inspecting and editing CSS, HTML, and Javascript live on any page. free
8. Watchfire Bobby: exposes accessibility issues. $299, 10 day free evaluation
9. JsUnit: testing framework for Javascript. free
10. Xenu’s Link Sleuth: checks for broken links. (Win) free
11. Vischeck: shows you what a webpage looks like to someone who is colorblind. free
12. Feng GUI: generates an attention  heat map on a webpage simulating how someone is likely to view the page. free
13. Fiddler: allows you to inspect all HTTP traffic between your computer and the internet, and "fiddle" with incoming or outgoing data. (Win) free
14. BrowserCam: provides screen captures of your website in multiple browsers and operating system, also provides remote access to testing machines. Pricing ranges from $19.99/day to $1000/year. Free 24 hour trial of the screen capture feature
15. RegexBuddy: for creating testing and debugging regular expressions. 29.95 Euro, 3-month unconditional money-back guarantee (ie. prepaid trial period)

Additional tools mentioned in the comments:

• DebugBar JSCompanion: IE developer tool
• XNView: image manipulation
• Colorzilla: Firefox color picker extension
• RegExpCoach: for regular expressions
• Notepad (with syntax coloring): for coding
• Pixeur : colorpicker
• Inkscape: opensource vector application
• WebXACT: Free online accessibility tool
• Aptana: Free opensource IDE 
  
• Sitevista : alternative to BrowserCam above ($29 a month)
• browsershots.org: free alternative to BrowserCam
• Komodo Edit:  editor
• Cyberduck: FTP agent.
• Pixie: colour picker

Also see:
See your site in IE on a PC - IE NetRenderer