Note: This article has done its job, and will be retiring soon. To prevent "Page not found" woes, we're removing links we know about. If you've created links to this page, please remove them, and together we'll keep the web connected.
To remove a hyperlink, select the item in your file, go to the Insert tab of the ribbon and click Link > Remove Link. (In Word it's Insert > Links > Link > Remove Link)
If you'd prefer to do this from the keyboard, select the link you want to remove and press +6. Note that this only works in Word.
Tip: If you want to remove multiple hyperlinks, press +A to select all text and then press +6.
However, this command doesn't remove hyperlinks from pictures. To remove hyperlinks from a picture using a keyboard shortcut, you'll need to use VBA macros. Here's more information on what macro to use.