Here are the main Firefox shortcuts I use on a regular basis.

Tabs
Ctrl-t – Open new tab
Ctrl-w – Close active tab
Ctrl-Shift-t – Open last closed tab (you can do this over and over)
Ctrl-PageUp, PageDown – Cycle through tabs
Ctrl-1 to Ctrl-8 – Go to the first, second, third…eighth tab
Ctrl-9 – Go to last tab

Other windows
Ctrl-h – Open history sidebar
Ctrl-b – Open bookmarks sidebar
Ctrl-Shift-b – Open bookmarks manager
Ctrl-j – Download manager

Browsing
Ctrl-l / Alt-d – Put cursor in the URL field so I can type a shortcut or URL
Ctrl-k – Put cursor in search field, or if it’s not visible, open default search in current tab
Ctrl-Enter – Add www. and .com to the string in the URL bar (if you type google, it will take you to www.google.com
Shift-Enter – Add www. and .net to the string in the URL bar
Ctrl-Shift-Enter – Add www. and .org to the string in the URL bar
Alt-Enter – Open address in new tab. (For instance, hit Ctrl-l on current tab, type a URL then Alt-Enter to open it in new tab)
Ctrl-r / F5 – Reload page
Ctrl-Shift-r / Ctrl-F5 – Fresh reload (doesn’t hit cache)
Alt-Left-Arrow – Go to previous page in history
Alt-Right-Arrow – Go to the next page in history

Search
/ – Open up quick find dialog at the bottom of the window
‘ – Open up quick find dialog for links only (once you’ve found the link you want, hit Enter to go there)
Ctrl-g – Go to next occurrence of search phrase
Ctrl-Shift-g – Go to previous occurrence of search phrase

Misc
Ctrl-d – Bookmark a page
Ctrl-Shift-d – Bookmark all tabs
F11 – Switch to full screen mode (Hitting it again returns to normal mode)

You can find the rest of them here.