Okay, this one took me a while to figure out, but nonetheless I found it and will share it.
In order to turn off or disable the MySite or MyLinks functionality you need to be an Sharepoint administrator.
Go to the Central Administration Web Page
Click on the link for Shared Services Administration
--If you have more than one SSP, select the one that is running the MySites functionality
Under "User Profiles and My Sites" click Personalization Services Permissions
Select the group you want to limit the functionality for. More than likely you will just have NTAuthority\Authenticated Users.
In the next screen you will see a list of checkboxes,
--To disable MySites uncheck "Create Personal Site"
--To disable MyLinks uncheck "Use Personal Features"
Once you find it, disabling the functionality is pretty easy, but if you are new to 2007 like I am it will take a while to find. Hopefully this will save you a few cycles.