From the Super Mario Wiki
Blue Shells are blue Koopa Troopa shells that first appear in Super Mario World. It is one of the only games where they are actually worn by Koopa Troopas. The Koopa Troopas turn around when reaching a ledge. They also walk faster. They are a rare type of shell, rarer than Red Shells. It can make any Yoshi fly instantly upon putting one in its mouth.
In Super Mario Strikers, as well as in Mario Strikers Charged, Blue Shells appear as items. They are usually collected in a pack of three. When used, they will be fired at the opposing players, however, they do not home in, like the Red Shell does. If the Blue Shell happens to hit a player, they will instantly freeze in one spot. This will render them unable to move, and, thus, unable to get the ball. The effects wear off after a few seconds. Unfortunately, these shells can freeze both the user's teammates, or the user. If the shells fail to hit anyone, they will continue bouncing around the stage until they either hit a player, or just wear out on their own. A more effective version of this item is the Giant Blue Shell.
In New Super Mario Bros., there is a Blue Shell item. It is not used as a weapon, but as a power-up. The shell turns Mario or Luigi into Shell Mario or Shell Luigi respectively (when collecting it or ground pounding the Koopa). When ducking, Shell Mario/Luigi is invulnerable to almost anything. Also, they can Shell Dash. Blue-shelled Koopa Troopas that leave Blue Shell power-ups when stomped on appear in multiplayer. They respawn periodically. Some obstacles can also only be passed by using the unique Shell Dash the power up offers. If a single Brick Block is protected on the top, bottom, but not the sides, the Shell can smash it allowing access to otherwise inaccessible areas.
Kooper from Paper Mario utilized a blue Koopa shell, which was initially stolen by Fuzzies before being retrieved by Mario. Although the next playable Koopa Troopa character, Koops in Paper Mario: The Thousand-Year Door, doesn't possess a blue shell himself, his father Koopley does, as did Kolorado's father. The Blue Koopa shell apparently is capable of resisting stomach acids from within a dragon's stomach tract for a long period of time, as evidenced by Koopley surviving being eaten by Hooktail by staying in his shell.
The Blue Shell appears in Mario & Luigi: Bowser's Inside Story, as an item found in the overworld and once in the Energy Hold in Bowser's Body. Mario can go in Blue Shells (and turn into Shell Mario from New Super Mario Bros.) by striking Blue Shell blocks. Luigi can then hit Mario using his hammer, and this will make Mario go into the shell, spinning straight forward. This can be used to hit blocks in areas which Mario and Luigi can't directly go into. To toss the Blue Shell, Mario must jump. It behaves similarly to Kooper and Koops's abilities in the Paper Mario series.