From the Super Mario Wiki
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Star Doors are doors that restrict progress to certain required parts of the game until the player has the necessary number of Power Stars. They have appeared in Super Mario 64 and its remake Super Mario 64 DS inside Princess Peach's Castle. Like most locked doors in these games, a certain number of Power Stars must be obtained before they can be opened (although Star Doors require many more Power Stars than regular doors). Once unlocked, the doors will slide open allowing Mario to enter. Only Mario can unlock a Star Door, but once it is unlocked, any character can enter it.
Four star doors exist in the games: