I have experienced this problem in Outlook 2010 recently. When I click on URL links in my emails, Outlook does not open them. It keeps on showing the thin blue bar at the top in the email, indicating that it’s processing to open the URL. But it never finishes. I did not have this problem before.
Guessing that this is a transient issue, I have closed Outlook and restarted it. After this, I could open URL links without any issue. If you are also experiencing this issue, you can try this quick workaround.