If you have encountered this annoying prompt when double-clicking on attachments in Outlook, fear not, there is a way to avoid it each time. This fix applies to Outlook 2007 and above (including 2013).
As with any increase in security, Microsoft has become tighter with security in Outlook in particular. Microsoft has set it to prompt you in case the file you are clicking on is a malicious attachment. The problem is, you can't uncheck the box so that you can just directly open the attachment. If you are running a decent antivirus program such as Nod32 or free ones like AVG or Microsoft's Security Essentials, then these attachments will be checked automatically by default.
Again, as a word of caution, only perform this action if you already have an anti-virus program installed on your computer that checks attachments for viruses and malicious code. And of course never open attachments from anyone you don't know.
The simplest solution to fixing this is to hold down the shift key while right clicking on your Outlook shortcut. Choose "Run as Administrator." Now go back to the email with the attachment in question and uncheck the box "always ask before opening this type of file" and click open.
After this, close Outlook and reopen Outlook as you normally would (no need to run as Administrator after the change is made, only when selecting a new file type to change). Now each time you double-click on that particular type of document whether its a .doc, .html etc, it will automatically open. Remember you will need repeat the Administrator procedure with each file type that you want to auto open on double click.