Helping people with computers... one answer at a time.
The Bing toolbar is apparently showing up unexpectedly for some people. I'll look at important terminology and how to get rid of the Bing toolbar.
I have to be honest - this question threw me for quite a loop. But after I'd received it for about the third or fourth time it was clear I had to figure out what was going on.
My initial reaction? Bing's a web site - http://bing.com - it's not something you "get rid of". If you don't like Bing, well then just don't visit that web site.
It couldn't be that simple, so I must be missing something.
What I was missing, of course, was that what people were really asking about was the Bing toolbar.
I hate to say it, but terminology matters. A lot.
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So to be clear:
Bing: Microsoft's search engine, available at http://bing.com. It's a direct competitor to Google.com.
Bing toolbar: software that is installed into your browser to add an additional toolbar to make using Bing easier.
You don't get rid of Bing, you get rid of the Bing toolbar.
Fair enough, except that Microsoft once again doesn't help when they use their own terminology incorrectly.
One way to get the Bing toolbar is directly from Microsoft:

The confusion begins right away as this one page uses three distinct terms to refer to the Bing toolbar:
Bing toolbar (on top)
Bing Bar (center title)
Bing (the "Get Bing Now" download button)
The last one is the worst offender. No wonder people are confused.
Since people seem to be surprised by the appearance of the Bing toolbar, I'm going to assume that it shows up in other ways as well. The most common culprit for toolbars in general is as a pre-checked "also install" option when you're installing something else completely unrelated. In the rush to get whatever that is installed, people just click "Next" until the install starts, not realizing that in doing so they've also explicitly asked for the Bing toolbar.
Regardless of how, it's installed.
Let's get rid of it.
Here's the toolbar in Internet Explorer after its default install:

The easiest way to hide it is to click the "X" to its left:

Click on that and you'll get this dialog:

As you can see it's asking if you're sure you want to disable the Bing Bar add on. "Bing Bar BHO" is just the Bing Bar add-on (BHO is Browser Helper Object). At the same time you're given the option of disabling other add-ons that were part of the Bing Bar install.
Click Disable and it's gone.
Gone, but not forgotten.
If you click on the Internet Explorer Tools menu, and then click on Manage Add-ons menu item you'll see that Bing is still listed as a disabled, but present add-on:

You can re-enable the Bing toolbar here if you wish. (You also could have come here to disable it in the first place.)
As you can see above, hiding the Bing toolbar doesn't really remove the Bing toolbar. For that we need to go elsewhere.
In Control Panel, click on Programs, Programs and Features to get to the Uninstall or change a program list:

And there it sits. Even though we've disabled it, it remains installed.
Right click on it:

And click on Uninstall.
After a few confirmations:

As I've written about before, the practice of "drive by installs" of toolbars and other software is both annoying and sadly common. In my opinion, it's really just another form of advertising in most cases. Whenever you install software, any software, you need to pay very close attention to all the options that are offered, and make sure that you are installing only what you want.
In actually downloading and installing the Bing toolbar for this answer, I was quite amazed at how much was downloaded. This is not a lightweight install, and for that reason if no other I would strongly recommend against it. It's just not worth it, in my opinion.
However, that's just my opinion. It's also a safe toolbar - as long as you get it from Microsoft or other reputable source it's not going to come with malware or the like.
Just make sure that it's something you do want.
And if you get it somehow, and you decide you don't want it, just uninstall it using the steps above.
I've added a new article on getting rid of one trace of Bing that the above article doesn't address: the search provider. That's the tool that powers the search box typically in the upper right of your browser window. See How do I really get rid of all of Bing? for more.
Article C4423 - August 28, 2010
Unable to uninstall "bing". Keep getting message "cannot remove bing bar right now. Try to uninstall later. ' I have been trying to uninstall for months. I have gone into programs and everything. Stii I can't get bing off mty computer.
Posted by: William Schuerman at January 23, 2012 3:19 PMwhen I highlight a name in an article to get more info on that name, a dropdown box appears and there is a box to click that says search with bing.
How do I change that to Google?
03-Feb-2012
I dont have a Bing toolbar,but the page keeps coming up when I try to get Internet Explorer.Cant find it anywhere to uninstall it.
06-Feb-2012
I have Internet Explorer, OPTIMIZED for BING and MSN...Please tell me, HOW do I get rid of that? I just want Internet Explorer. Had NOTHING but trouble since Bing Showed up. Why would anyone want BING?
Posted by: Jan at March 17, 2012 5:40 AMI HATE BING!!! IT'S LIKE AN UNINVITED, INVASIVE PARASITE. HOW I GOT IT IS ANYONE'S GUESS. BUT NOW THAT I'M INFECTED I CAN'T GET "CURED," NO MATTER WHAT I DO. SHOULD I JUST THROW MY I-MAC OUT THE WINDOW?
FRUSTRATED AND ANGRY,
Posted by: Nicholas at May 12, 2012 3:21 AMNAP