Firstly, you shouldn't have a <p> (a block level element) inside an <a> (inline element). Not sure why word-wrap would be relevant here, but try this setup instead:
Code:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Experiment</title>
<style type="text/css" media="all">
#twitter-follow {width: 410px;height: 44px;float: right;clear: right;margin: 0 25px 20px 0;padding: 0 15px;}
#twitter-follow a img {margin: 0 5px 0 0; vertical-align: middle; border: none;}
#twitter-follow p {padding: 0; margin: 0;}
a {text-decoration: none;}
</style>
</head>
<body>
<div id="twitter-follow">
<p><a href="http://mysite.com"><img src="/images/twitter.png" width="37" height="35" alt="Twitter">Follow me on twitter</a></p>
</div>
</body>
</html>
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