From the Super Mario Wiki
Thunderbolts (also called Lightning, Lightning Bolt, or Shock) are attack items found in the Mario Kart and Paper Mario series. These special items summon lightning from the sky, causing various effects.
Mario Kart series
In the Mario Kart series, Thunderbolts are extremely powerful items that racers usually receive when they are in (or near) the last position in a race. When used, a thunderbolt will temporarily shrink all the other racers, making them slower and weaker. It also temporarily makes the racers' voices high-pitched and sped up until being back to normal or getting squashed. It is also the emblem for the Lightning Cup.
In Super Mario Kart and Mario Kart 64, if any shrunken players are driven over, they will be squashed and unable to move for a few seconds. While shrunk, the character's weight is equal to other shrunken players. If two shrunken players run into each other in Mario Kart 64, they will both crush each other.
In Mario Kart: Double Dash!!, the thunderbolt can also scatter racers' items across the road when used. However, the item does not affect players that are currently indisposed (such as having just been hit by another item, or having fallen over a cliff). Also, unlike in Super Mario Kart and Mario Kart 64, shrunken players will not get squished if they ram into normal sized racers. However, tiny karts will be easy to push around, even by the Bullet Blaster, the lightest kart in the game.
In Mario Kart DS, the effect of being hit by a thunderbolt wears off much faster depending on the rank that the player is in. For example, someone hit by one while in 7th place will return to normal almost immediately, while those in 1st or 2nd place will remain shrunk for up to six seconds.
In Mario Kart Wii, as in Mario Kart DS, the effect of the thunderbolt lasts more briefly the lower the rank the player is in. Also, players who get hit by other items can still be affected by this item. If the players are under the effects of a Mega Mushroom, they will shrink in size to a normal sized player.
In Mario Kart 7, as in Mario Kart DS and Mario Kart Wii, the effect of being shocked by the thunderbolt will last determined on the level rank the player is in, from last place decreased time and in first place will last the longest. As before, the theme of the current track will be altered and even hit by another item, the player will still go into effect. Any players that are shrunk will also be squished if run over by normal sized racers, an effect returning from Super Mario Kart and Mario Kart 64. Unlike in Mario Kart Wii, when a driver is shot out of a cannon, the shrinking effect will still happen and the driver will fall while gliding midair.
Since Mario Kart 64 until Mario Kart: Double Dash!!, when a thunderbolt is used, a sound like that of a tiny alarm is heard during the effect of the thunderbolt. In Super Mario Kart that sound is only heard when the thunderbolt is launched, and in Mario Kart DS, Mario Kart Wii and Mario Kart 7, the music in the race is affected when the player is hit by the thunderbolt. In Mario Kart 7, the extra beat that plays in 1st place goes out of sync with the music for a few seconds after the attack.
The Thunderbolt's effect can be avoided if a racer has a Mega Mushroom, Star, Boo, or Bullet Bill item activated when the bolt strikes, or if they are flying through the air after being shot out of a cannon (except in Mario Kart 7).
Paper Mario series
In the Paper Mario series, the attack item is known as a Thunder Bolt. This item summons a bolt of lightning that inflicts five damage to one enemy. But if used on lightning related enemies such as Dark Puffs, they will gain HP.
Also, in the series is the much more powerful Thunder Rage. This item summons a lighting storm that inflicts five damage to all enemies.
Super Smash Bros. series
Lightning appears in Super Smash Bros. Brawl as an item. The item was confirmed by the E for All demo and it also appears as a Sticker. The item usually shrinks all of the player's opponents. However, at times it might backfire and shrink the player who grabbed the item. Lastly, there may be a case in which the item might actually make the opponents giant sized (it's just like the Super Mushroom, only it's twice as effective).
An interesting note to point out is that players that get shrunk by the Lightning will be smaller than when they touch the Poison Mushroom. Likewise, if players become giant from the Lightning, they will be much bigger than when they grab a Super Mushroom.
In Mario Hoops 3-on-3, the Thunderbolt plays much the same purpose, stunning all players and making the ball drop out of one's grasp. In Mario & Sonic at the Olympic Games it appears in the Dream Races where it also makes characters shrink and slow down. In Mario Power Tennis, the thunderbolt appears as an item in the Item Battle in Exhibition Mode. It has the same effect as it does in the Mario Kart series. It shrinks the player's opponent(s), making them unable to run faster to get the ball. In Mario Superstar Baseball, it is one of the items resulting from landing the ball in the ? space. If the player receives that, they will switch with the leading player's coins with their coins. In Mario Super Sluggers, it appears as an error item, but only in Toy Field, where the losing player may receive it. If the player uses it, all fielders would get stunned by it while the player may get coins resulting from the stun. In Mario Party 9, Thunderbolts appear in King Boo's Puzzle Attack. Lining three of them will cause a lightning that will reduce the opponents points by one, and will give more damage to King Boo than other objects. It also appears in Mario Party Island Tour, known as Lightning Score Striker, it subtracts three from a opponent's roll and only appears in the Perilous Palace Path board.
A Thunderbolt cameos on the wrapper of Cashzap Candy in Mario Party 8. In Super Mario World and New Super Mario Bros. U, the enemy Sumo Bro. use thunderbolts to attack. Thunderbolts appear as items in Mario Pinball Land too.
In Mario Party: Island Tour, Thunderbolts are referred to as Lightning Score Strikers and subtract 3 from an opponent's roll.
Trophy Information from Super Smash Bros. Brawl
Names in other languages