Good list: The most popular and most functional Firefox extensions:

1. Block ads on webpages : Adblock Plus
2. Use mouse gestures (powersurfing) : All-in-One Gestures
3. Download manager in a statusbar : Download Statusbar
4. Customize Google pages; remove ads : CustomizeGoogle
5. Discover interesting sites being recommended by others : StumbleUpon
6. Manage tabs (multiple links/duplicate/close etc ) : Tab Mix Plus
7. Look up any word in dictionary : Answers
8. Translate pages : Translator
9. Download videos : Video DownloadHelper
10. Block Flash ads or content : Flashblock
11. Blog about the current page : Performancing for Firefox
12. Clear the cache with one click on the toolbar : Clear Cache Button
13. Surf the web without leaving a trace in my computer : Stealther
14. View an Internet-Explorer-only webpage in Firefox : IE Tab
15. See weather information : ForecastFox
16. Download/upload files using ftp : FireFTP
17. Speed up Firefox : Fasterfox
18. Blog to Blogger service : BlogThis
19. Synchronize Firefox bookmarks on different computers : Bookmarks Synchronizer
20. Bypass mandatory registration of username and password for sites : BugMeNot
21. Be notified when new mail arrives at Gmail account : Gmail Notifier
22. See thumbnails of pages in session history : Reveal
23. Store and sync bookmarks online : Chipmark
24. Chat on the Internet Relay Chat (IRC) : ChatZilla
25. Minimize Firefox to system tray : MinimizeToTray
26. Use Gmail for space : Gmail Space
27. Add/remove/change some features for sites : GreaseMonkey
28. Block phishing sites : NetcraftToolbar
29. Control iTunes using Firefox : FoxyTunes
30. Use a sidebar to control multiple functions : All-in-One Sidebar
31. Open PDF files in a new tab : PDF Download
32. Save all the images/media on a page : Magpie
33. Zoom in/out on an image : Image Zoom
34. Search the bookmarks : Locate in Bookmark Folders
35. Manage user styles for sites : Stylish
36. Edit bookmarks easily : Flat Bookmark Editing
37. Download/open all/selected links on a page : Linky
38. Add a powerful multi-functional preference bar : PrefBar
39. Add more search engines to Firefox search box : Mycroft
40. Create a tiny url : TinyUrl Creator
41. Track time spent browsing / on a project : TimeTracker
42. Add RSS feeds to web-based/desktop readers or reader extensions : LiveLines
43. Search up to 25 custom chosen sites : Roll your Own Search for Firefox
44. See Alexa information, search engine backlinks for a page : SearchStatus
45. Fill web forms with name/address/email etc : Autofill
46. See all tabs in one window : Viamatic foXpose
47. Automatically copy the selected text to clipboard : AutoCopy
48. Change user agent for certain sites : User Agent Switcher
49. Find the meaning of selected word in a dictionary : DictionarySearch
50. Create new different passwords for different sites : PasswordMaker