Links corrupt on send
When you create a mailing with CiviMail, there's an option:


  Track Click Throughs
  
  Track the number of times recipients click each link in this mailing.
  
  NOTE: When this feature is enabled, all links in the message body will
  be automatically re-written to route through your CiviCRM server prior
  to redirecting to the target page.


Perhaps you have enabled this option? This wouldn't normally prevent the links from working, however.

Are the links in the email something like, http://mysite.com/sites/all/modules/civicrm/extern/url.php?u=123&amp;qid=12345 ? If so, that is normal when tracking click throughs is enabled.

What happens when a user clicks on one of the links?

Which CiviCRM version and CMS (Drupal, Wordpress or Joomla) are you using?