From the Super Mario Wiki
The Crystal Stars are the seven stars Mario, Goombella, Koops, Flurrie, Yoshi, Vivian, Admiral Bobbery and possibly Ms. Mowz collect in Paper Mario: The Thousand-Year Door. They open the Thousand-Year Door to the Palace of Shadow and will teach Mario seven special moves. They consist of the Diamond Star, the Emerald Star, the Gold Star, the Ruby Star, the Sapphire Star, the Garnet Star and the Crystal Star.
The stars were created by the Shadow Queen to hold the essence of the heavens, but the four heroes collected them and used their power against the Queen. One of the castles built to hold the stars is Hooktail Castle.
Hooktail has the Diamond Star, the Puni Elder has the Emerald Star (Mario had to defeat Magnus to get it), Grubba has the Gold Star, Doopliss has the Ruby Star, Cortez has the Sapphire Star, Pennington has the Garnet Star in his home, and Magnus 2.0 (Lord Crump) has the Crystal Star.
There are also two fake Crystal Stars, one on Rawk Hawk's belt, and another held as a decoy in the Poshley Sanctum.
The stars bear much resemblance to the Seven Stars in Super Mario RPG: Legend of the Seven Stars.
The Crystal Star' Powers
|Rogueport in a small chest, with a merchant
||No one; given to Mario by Princess Peach
||Replenishes up to 7 HP for both party members and 8 FP, as well as curing all status effects.
||If successful, this power creates an earthquake that can do up to 6 damage against all enemies.
| Emerald Star
|The Great Tree
|| Puni Elder
||If successful, immobilizes all enemies temporarily.
| Gold Star
||Boosts attack and defense power for a short time for both party members.
| Ruby Star
||Any amount of damage can be done depending on how many times the player encircles around the enemies
| Sapphire Star
||Much like Sweet Treat, the player will replenish up to 24 HP for each party member and 24 FP.
| Garnet Star
||Pennington (guards the Poshley Sanctum)
||If successful, destroys enemies in a single blow. NOTE: Does not work on enemies with more than 12 HP, mini-bosses and bosses.
| Crystal Star
|X-Naut Fortress, originally in Rogueport
||Possibly originally no one, Magnus von Grapple 2.0
||Does up to 15 damage to all enemies, 3 each time the player fills the gauge.
Names in other languages
|From English "Star Stone"