We gathered all Facebook widgets into one place to make your Facebook widget search easier.
Facebook Official Widgets
Personal Profile Widgets:

Profile Badge: Share your Facebook information on other websites. Three display configurations and 15 information choices.
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Photo Badge: Share your Facebook photos on other websites. Three display configurations. Share up to 8 photos.
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Fan Badge: Show off your favorite Pages on your website or blog. No display configuration. Only shows one page that you are a fan of.
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Website or Business Widgets:

Share: Let visitors to your site share your content on Facebook. Button or link style. With or without a counter. Custom linking options.
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Fan Box: Allow users to become your fan and view your Facebook Page stream. Choose whether to display your fans and your Facebook stream. (Currently in widgetslab sidebar)
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Page Badge: Share your Facebook Page information on other websites. Three display configurations and options to share Name, Status, Profile Picture and Fans.
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Twitter Link: Automatically post your Facebook status updates to Twitter. Status Updates, Photos, Links, Notes and Events can be shared or unshared.
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Developer Widgets:

Publishing to Facebook: Let users publish their actions and content back to Facebook. Custom image options available.
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Comments Box: Allow users to easily comment on your content. No real options.
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Live Stream: Allow Facebook users to connect, share and post updates in real-time. No real options.
http://www.facebook.com/facebook-widgets/
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Google Gadgets for Facebook

Facebook – Now with Full-Screen viewing
Also from iBuno.net http://www.ibuno.net/gadgets/facebook.html
Fully-Featured Facebook Gadget: your essential miniaturized facebook connection. View your news feed, inbox, photos and stay all connected to all your facebook friends directly from your iGoogle page or your web site, all in this convenient gadget. Now with convenient canvas view you can maximize the gadget to gain access to the full facebook site; just click on the maximize button in the upper right hand corner.
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myFacebook Chat!: Simply allows you to add the Facebook Chat window to your web site or blog. Probably works on igoogle pages as well. Warning…this removes chat from your Facebook page while you are viewing it.
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Facebook iPhone Edition Google Gadget

iPhone Edition Google Gadget for your web site.
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Miscellaneous Widgets
VentureBeat Profiles widget for Facebook
This is a company profile that indicates things like Location, number of employees, financials etc. There is even a current news feature that updates. This is a great addition to any post about Facebook.

Grab the basic code.
Go to VentureBeat Profiles for full widget customization options.
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the Social Blog Badge from Mighty Widgets
This widget allows you to create links to many of your social pages. Facebook is not alone here!

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Yahoo! Desktop Widgets (need Yahoo! Widgets install)
Facebook(er) Yahoo! widget

Get Faecbook(er) widget
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Facebook Notifier Yahoo! Widget

Get Facebook Notifier widget
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Mac Dashboard Widgets (requires Mac OS X and Dashboard)
Facebook Alert for Mac OS X Dashboard

Get Facebook Alert for Mac OS X Dashboard
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Facebook Dashboard Widget for Mac OS X Dashboard

Get Facebook Dashboard Widget for Mac OS X Dashboard
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Facebook Watch for Mac OS X Dashboard

Get Facebook Watch for Mac OS X Dashboard
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Facebook Widget 0.5 for Mac OS X Dashboard

Get Facebook Widget 0.5 for Mac OS X Dashboard
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Windows Sidebar/Live Gadgets
Facebook Explorer for Windows Gadgets

Get Facebook Explorer for Windows Gadgets
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Facebook3 Windows Live Gadget

Get Facebook3 Windows Live Gadget or here Facebook Sidebar
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Facebook Sidebar Gadget

Fast and easily change your status. See all notifications sent to you.
Hassle free login, simply login to the gadget once and keep yourself logged in all the time!
Simply click the links within the gadget to open up the notification in your browser!
Get Facebook Sidebar Gadget or here Windows Live Facebook sidebar Gadget
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My Facebook Gadget

Get My Facebook Gadget
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Google Desktop Gadgets
Facebook Gadget

Get Facebook Gadget
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Facebook Friends Gadget

Get Facebook Friends Gadget
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Slideshow for Facebook

Shows random photos from your friends on Facebook
Get Slideshow for Facebook
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Conclusion:
As you can see, there are many Facebook Widgets, Gadgets and more. There are even Facebook desktop apps which I considered adding here. I decided to draw the line at Desktop Widgets/Gadgets.
If you know of any that are missing…please comment so I can add them to the list.
Thank You.