Sometimes it's not clear when an application requires a privileged certificate or not. Here's a high level overview of the reasons you would need your application to run privileged:

Only privileged processes can:
  • Create, modify, or delete SYSTEM files
  • Create, modify, or delete protected registry keys
  • Create, modify, or delete databases with the SYSTEM flag.
  • Access several system APIs, for example:
    • CryptProtectData with the CRYPTPROTECT_SYSTEM flag
    • Several IOCTL calls including rebooting and querying the device unique ID
    • Make calls directly to the radio using TAPI

There's a more detailed list like this in MSDN under Trusted APIs