Basics:

  Firebug
  https://addons.mozilla.org/en-us/firefox/addon/firebug/
  
  YSlow
  https://addons.mozilla.org/en-us/firefox/addon/yslow/

CSS Helpers:

  CSS Reloader
  https://addons.mozilla.org/en-us/firefox/addon/css-reloader/

  Firepicker
  https://addons.mozilla.org/en-us/firefox/addon/firepicker/
  
  FireDiff
  https://addons.mozilla.org/en-us/firefox/addon/firediff/
  

Proxy/HTTP:

  Tamper Data
  https://addons.mozilla.org/en-us/firefox/addon/tamper-data/
  
  FoxyProxy
  https://addons.mozilla.org/en-us/firefox/addon/foxyproxy-standard/
  
  Charles Proxy (has an autoconfigure add-on)
  http://www.charlesproxy.com/
  

Database:

  SQLite Manager
  https://addons.mozilla.org/en-us/firefox/addon/sqlite-manager/