If you are not receiving any visual voicemail notifications, or are receiving random texts from a 9016 shortcode, follow these steps to re-register your device with the Visual Voicemail system. If these steps do not resolve the issue then Customer Care/Technical Support will need to check the network side to ensure everything is setup correctly on the account.
EDIT: In some cases, third-party messaging applications like Handcent, GoSMS, etc. could intercept the text messages before the VVM application does. Check the messaging application to see if it has a compatibility setting that may prevent this behavior. You may need to uninstall the messaging app, re-register with the VVM server, and then reinstall the third-party app to fix the interception issue.
EDIT 2: If you use a third-party messaging application (GoSMS, Handcent, or similar) and are having issues, follow the below instructions:
If you have Go SMS you will need to disable the "disable other text notifications"
If you have Handcent, you will need to go into Handcent, press menu, settings, application settings, default messaging applications and then check "disable".
If you use another application, check for a similar setting that could be causing the issue.