This doesn't happen for me in IE8 and I've never spotted it. I also can't find it in the Internet Options anywhere.
It is possible that you have some software on your computer that does this, for example AVG Anti-Virus adds content to web pages to tell you that it has checked the links being displayed for potentially harmful content - so your system-security software may be expanding all links to show you where they actually point, to prevent phishing attacks.
If you do have some anti-phishing software on your machine, you'll have to find the option within that.
Update - It is almost certainly some clever CSS.
I have created the following test page to demonstrate how you can add the URL to a link using CSS generated content. If this was used within a print stylesheet, this would explain how the URL is getting added to the link when you are printing the page. To stop this, you would have to save a copy of the web page, remove the style rule from the print-only style sheet and then open your copy and print it!
<html>
<head>
<title>Test</title>
<style type="text/css">
a:after {
content: " [" attr(href) "] ";
}
</style>
</head>
<body>
<h1>Test</h1>
<p>This is a test to see if this
<a href="http://www.stevefenton.co.uk/">Link Shows A URL</a></p>
</body>
</html>