For Movieplayer under Quicktime 3, or Quicktime Player 4:
Open the Date & Time control panel.
Set the date several years into the future.
Launch the MoviePlayer or Quicktime Player.
When the Upgrade dialog appears, click on Later (much later!).
Quit the Player and reset the year in the Date & Time control panel.
That's it! You won't have to worry about the Upgrade message for the next several years!
Nate Hamilton suggests this way to stop the upgrade nag screen when using Quicktime Player 4.0
Open QuickTime Player, and from the Help menu, select '"Check for Updates". In that dialog, simply check "Don't notify me of updates". Problem solved for good, until you want to turn it back on again.
