Bob-ombs, (ボム兵 Bomuhei, Bomb Soldiers), are items that has appeared in any game of the Super Smash Bros. series. They will explode on contact when hit or thrown. After a short time, they will start walking back and forth on the stage and then will stop, turn red and explode. In Super Smash Bros. Brawl, picking them up activates the timer, causing it to explode in one's hand if one does not throw it in time. Bob-ombs are quite dangerous items, as they do severe knockback on contact with players. Even a player who grabs a Bob-omb must be careful, as it is very easy to KO oneself if one throws the item too close, or sometimes if one is struck by a projectile while holding the bomb.
In Sudden Death, Bob-ombs fall randomly from the sky if the match takes too long. These Bob-ombs are slightly larger than normal and (despite what most believe) can be grabbed through grabbing the item in the air. The falling Bob-ombs are absent in Super Sudden Death.
If six Bob-ombs are detonated at the same time, a large explosion will occur, normally a one-hit KO. The same effect can be used with Blast Boxes, only the effect is more powerful and requires a trigger.
When a Bob-omb starts walking after being left alone for awhile, it normally will explode on contact. However, if the player shields when the bomb is walking towards them, it will walk harmlessly past them.
In Super Mario Bros. 2, Bob-ombs were bomb-like enemies that walked around and blow themselves up. The Bob-omb could also be picked up and thrown at enemies. Bob-ombs reappeared in Super Mario Bros. 3, and if the player jumps on a Bob-omb it would become stationary. The player could also pick up the Bob-omb and throw it at enemies; however, the Bob-omb will explode after a few seconds after being jumped on. In Super Mario 64, if the player gets close enough to a Bob-omb, it will ignite itself and chase after the player. They could also be picked up and thrown, but they will explode immediately after hitting the ground.
In the Smash Bros. games, a Bob-omb will stay at a spot for a short period of time. After the short period of time, it will walk around and self-destruct. The Bob-omb exploding on contact to whatever it hits is a reference to their behavior in Super Mario 64. 
 Description from the Super Smash Bros. Instruction Booklet
When grabbed and thrown at an enemy, this item explodes, but if left alone, it will start walking around until its timer reaches zero...
 Melee trophy
 Brawl trophy