StumbleUpon is considered a legitimate toolbar and is quite different from Links.
What version of IE? If 7, simply go to Tools > Manage Add-ons > Enable or Disable, then disable it. I think Firefox has similar add-on manager, but I can't remember. In IE6, go to Tools > Internet Options > Programs tab. Then select the Manage Add-ons button.
Now "Links" is part of IE, going back several versions and it is a simple way to use your favorites more easily - I use Links extensively, with folders on my Links toolbar and many favorites within. But if you don't want the Links tool bar either, just Right Click on a blank spot in toolbar and uncheck Links.