Summary: Sometimes you just want to clear the things you've searched for from automatically appearing in the browser. These steps clear that information in Firefox.
I saw your article on clearing the search history in Internet Explorer 6. I use Firefox; how do I do the same thing?
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Firefox is actually easier and a little more intuitive. While we're at it, we'll include the Google Toolbar extension to Firefox as well.
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The Google Toolbar is pretty much the same as its IE equivalent. If you click on the Google logo on the far left you'll get a drop-down menu:

Click on Clear Search History, and that's done.
Now, for Firefox itself (I'll assume Firefox 2.0, by the way) a quick click on the Tools menu shows this:

Clear Private Data looks encouraging, but before you click on it, click on Options instead. Click on the Privacy tab, and you should see this:

Note the Private Data area, and the Settings... button to the right. Click on Settings... and you'll get a dialog that includes this:

Here you can control exactly what it is you want Firefox to clear when you tell it to "Clear Private Data". Most of what people seem to care about is their browsing history, but Saved Form Information is what you want if you're looking to erase the tracks of what you've been searching for using the Google home page.
So, make your selections as you wish, OK your way back out, and then go ahead and hit that Clear Private Data menu item on the Tools menu, and you should be good to go.
Remember: this has only dealt with Firefox. You may still need to return to IE and perform the equivalent there, since IE is used in many places throughout Windows, and some of its settings and/or history appear to be shared with some Windows features.
Related:
How do I delete history items from my Google tool bar? Deleting Google history takes a few steps, depending on what Google history you mean. Here are step-by-step instructions for deleting Google history.
How do I delete items from Internet Explorer's auto-complete list? Internet Explorer tries to be helpful by showing you recently visited URLs so you don't have to retype them. But what if you don't want them to show?
Article C2832 - November 7, 2006
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Thank You So Much Paul
I could not figure out at all how to clear the address bar in FireFox 3. It was driving me nuts!
Amazing how outdated information can get and/or why can't we get relavent information up sooner?
Posted by: Bobby the K at January 8, 2009 3:21 PMThanks Again!
In Firefox, if you want to delete an individual entry from the History,url just highlight it (either in the History sidebar or in the address bar drop-down) and press Shift+Delete. Gone
Posted by: Steve at March 3, 2009 9:10 PMdownload hide unvisited from firefox...it will clear the drop down box
Posted by: Freda at March 27, 2009 6:02 AMHere is the URL for the add on
https://addons.mozilla.org/en-US/firefox/addon/7429
Posted by: freda at March 27, 2009 6:04 AMFreda,
Posted by: Dan at April 21, 2009 8:12 AMWOW! Thank you so much for the URL for Firefox add-ons. I have tried everything to clear my search history, but this is the only one that worked. Thank you so much for sharing.
STEVE - You're awesome! Such a simple technique to delete the address history and it makes me love Firefox even more! Thank you so much because nothing else works in the new version of Firefox.
LEO: Thank you so much for posting this article. Great information (although not so simple in the new version of Firefox) and great way to learn from others with the same issues.
Posted by: SMP at May 25, 2009 9:44 PMSTEVE: Okay, sorry, I did it and it worked, however, everything came right back again. AAARRGHHHH!!! Why is Firefox being so difficult about this? :(
Posted by: SMP at May 25, 2009 9:48 PMOn the newest version of Firefox there's a separate option called 'remember what I've searched for' that's also under the preferences-privacy option. Worked like a charm. Thanks Leo!
Posted by: Lou at August 5, 2009 8:57 AMHi,
My company has created a product that could solve this problem. Our software, ControlHistory allows you to selectively or completely delete your history. You can download it from www.controlhistory.com. It supports
IE (ver. 6+)
Firefox (ver. 3+)
Chrome (ver. 1+)
Google Desktop Search
Many programs like MS Word, Excel, Acrobat Reader, WinRAR, 7-Zip, etc. that save their history in the Registry.
You can use the software for free to view your history but to be able to delete it you need a license. The cost of a license is USD 0.99 (99 cents).
Posted by: controlhistory at August 19, 2009 4:29 AMThank you, Leo! Yours is the ONLY site that I found that clearly communicated the answer!
Posted by: Christian at September 13, 2009 10:00 PM