Firefox: If you've noticed the pinned-tab feature in Google Chrome and would like to give it a try in Firefox, Pin Tab adds a simple and lightweight pinning feature to Firefox.
Once you've installed Pin Tab you can CTRL+Click on any tab to pin it to the left hand side of the tab bar—the keyboard combination can be altered or made into simple a double click if you prefer. Once you have a tab pinned to the side of the screen you can — in addition to the keyboard shortcut — simply drag a tab over into the pinned area and it will become pinned as well.
Pinned tabs can be shuffled within the corralled area, but once you drag them from the other pinned tabs they'll return to their previous state as fully expanded tabs. If you have Firefox set up to remember browsing sessions your pinned tabs will stay pinned in between uses.
One area where Pin Tab falls short from Faviconize, the Firefox extension that pre-dates Chrome's pinned tabs by a long shot, is the ability to automatically include tabs into the pinned zone. Check out Faviconize if you want white-list based automatic pinning.
Pin Tabs is free and works wherever Firefox does.