From the Super Mario Wiki
Fire Breath is a move Bowser can execute in various games. He will emit fire out of his mouth and burn anyone near. It is Bowser's signature attack.
Fire Breath is also one of Bowser's special moves in Super Smash Bros. Melee and Brawl. Bowser uses this move when the Button is pressed. It is exactly the same as a Fire Flower, except that the flames get smaller the more it is used. The attack is somewhat of a long-distance move, and is usually best to use when the enemy is coming in for close-range combat. However, the move will leave Bowser motionless while using the attack, and will leave his back open for attack. If Kirby copies Bowser's abilities, he will gain the Fire Breath attack.
Bowser also uses this move in Super Paper Mario and it is his special move in the game. It can be used to light candles. Also it can attack enemies from a distance, giving Bowser a slight advantage.
In Mario Power Tennis the Fire Breath is the Offensive Power Shot used by Bowser. It involves Bowser breathing fire on the ball and sending it over the court alight. A similar move was seen as Bowser's special shot in the Dream Table Tennis event in Mario & Sonic at the Olympic Games.
Fire Breath is also one of Bowser's commands in Mario & Luigi: Bowser's Inside Story. When used in battle, Bowser will inhale and when his face turns red, the player must press and hold or to execute the technique, burning any enemy in his path. The attack can also be used out of battle by pressing to ignite Launch Fits, burn trees and flowers, and more. However, when Bowser first appears in Cavi Cape, he is unable to use this ability due to (as later found out in Plack Beach) a Scutlet clogging his Flame Pipe. Once the Mario Bros. defeat the Scutlet, Bowser's Flame Pipe returns back to normal and he can breathe his fire again.