So, one of my users on my personal Google Apps domain (my Dad) asked the same question that I had written off as a normal inconvenience of using web-based email. Not having an actual, physical application my desktop to associate with the mailto: links on webpages means that every time I click on a link an unconfigured Outlook fires up. Annoying. And then my Dad asked me about it, so I had to get to the bottom of this.
After a little searching I found that there is Gmail Notifier and other like applications, but they seem to only work with Gmail accounts, not Google Apps hosted email accounts. Then I found this article, which I'm summarizing and reprinting, just in case the Google Support Forum goes away, and to make this easier to find in search engines.
Edit the following text and make it into a reg file before applying it by replacing yourdomain.com with your Google Apps hosted email domain.
Save the above text as a .reg file. Then double click on it to import it into your registry.
Lastly, go into your Internet Options in Internet Explorer and change your default MAILTO application to the new Gmail application.