“Here, have some bombs!”
Generally speaking, bombs as depicted in the Mario series are not entirely unique, and are based on a widely-used cartoon gag that stylizes bombs as sometimes being less dangerous than a real-world one and often depicts them simply as dark, round orbs with fuses atop them. Bob-ombs are living enemies based on this stylization as well. Despite appearing in recent games such Mario vs. Donkey Kong 2: March of the Minis, Bombs seem to be slowly fading out of the Mario series, being replaced by the aforementioned Bob-ombs (which function very similarly to the bomb items).
Mario's Bombs Away
Mario has to deliver bombs to his comrades at a military outpost, being careful not to blow up his own base.
Super Mario series
Super Mario Bros. 2
In Super Mario Bros. 2, Mario, Luigi, Princess Peach, and Toad can pluck bombs from the ground and throw them. In Super Mario Bros. 2, the four heroes have to use the bombs to clear obstacles in places like caved in areas. They can also be used to defeat enemies (though they can hurt the heroes as well). Bob-ombs also make their first appearance in the Mario series in this game, and can be found in later levels of the game. Enemies like Mouser attack by throwing bombs at Mario and his friends during their battles. Bombs later appear in remakes of Super Mario Bros. 2, such as Super Mario All-Stars and Super Mario Advance. These remakes changed them from red to purple.
In later installments of the Super Mario series, bombs are seemingly replaced by the Bob-omb enemies.
New Super Mario Bros. U
Bombs make a reappearance in the Super Mario series in New Super Mario Bros. U, in which bombs are Lemmy Koopa's main weapon of choice. Similar to Mouser in Super Mario Bros. 2, Lemmy throws the magically spawned bombs in an arch-like pattern. However, unlike the previous battles, these bombs bounce upon coming into contact with the ground, and if Mario, Luigi, Blue Toad, or Yellow Toad touch a bomb, it explodes immediately.
The bombs in this game appear to be purple in color (much like the redesigned bombs in Super Mario Advance), though they are decorated with yellow stars around them.
Super Mario 3D World
Bombs reappear in Super Mario 3D World, with a very basic design. They can be carried and thrown by Mario, and explode as they touch something after being chucked. also in-game are bomb variants reminiscent of soccer balls: rather than picking these up, Mario kicks them on contact, deflecting them. These soccer balls play an integral role in defeating Bowser in his Bowser Mobile in World 1 and World Castle of the game.
Club Nintendo Comic series
In Wario's Woods, the use of bombs are Toad's main form of attack when fighting the various monsters that were sent by Wario. Toad receives these multicolored bombs from his fairy helper, Wanda. In order to defeat Wario's minions (as well as the bosses in the game), Toad has to stack the bombs according to their colors; if the color matches a monster's color, it gets destroyed. In the SNES version of the game, Toad can be seen throwing a bomb at Wario's castle in the ending of the game, causing his castle to get destroyed and allowing peace to return to Wario's Woods, as well as the entire Mushroom Kingdom.
Bombs known as Smiley Bombs later appear in Wario World. They are purple in color and are shot out by Ankirons. While they strongly resemble regular bombs, they have faces painted on them. They also make an appearance in Mario Hoops 3-on-3. The defending team can sometimes receive one out of the ? Panels on the court. When thrown, they explode, knocking everyone within the blast radius down and spilling some of their collected Coins.
Wario Land: Shake It!
Bombs appear in Wario Land: Shake It! in Boogie Mansion, and are thrown by Peek-a-booms. There is also a bomb block that can be a platform before it explodes. Both can be triggered when touched or when Wario does an Earthshake Punch.
In Luigi's Mansion, bombs appear as large, normal-looking bombs with a skull emblem on them. Purple Bombers will drop a bomb once they are discovered, and bombs are also one of the things Boos will place in rooms (the other being a Boo Ball), which the Boo Radar will pick up as a Boo reading. Luigi can easily get rid of bombs by spraying the Water element at them, or he can simply avoid them.
Luigi's Mansion: Dark Moon
In Luigi's Mansion: Dark Moon, bombs first appear in the Old Clockworks. Ghosts will try to throw them towards Luigi, and in some rooms, if Luigi checks furniture, a bomb will pop out. In the ScareScraper, Bomb Brothers shield themselves with large bombs that must be removed so that they can be flashed with the Strobulb. Bomb Brothers also repeatedly drop smaller bombs while being vacuumed with the Poltergust 5000.
Super Smash Bros. series
Certain characters that appear in the Super Smash Bros. series, including Link, Young Link, and Toon Link, can throw bombs to attack. Bombs are also referenced in Super Smash Bros. Melee and Super Smash Bros. Brawl. When Peach tries to pull a vegetable from the ground, she may occasionally grab a Bob-omb. The way she plucks a Bob-omb makes reference to the way that she and the other heroes pulled bombs from the ground in Super Mario Bros. 2.
DK: Jungle Climber
Bombs also appear in DK: Jungle Climber, where they can be used and thrown in order to destroy obstacles such as Steel Kegs. In later levels, bombs serve as a semi-common weapon used by Kritters to attack.
Paper Mario series
Super Paper Mario
In Super Paper Mario, there is a bomb-shaped Pixl named Boomer that Mario can use to blow up switches, blow up cracks in walls, and defeat enemies. Bombs also appear occasionally when a player stomps on a Ninjoe, a Ninjohn, or a Ninjerry. These bombs look exactly like Boomer, though unlike Boomer, they can hurt the player. A bomb later appears in Chapter 6-2, when Mimi disguises herself as King Sammer and tells the player to open a chest in front of them. There's a bomb inside the chest, but it turns out to be a dud.
Paper Mario: Sticker Star
In Paper Mario: Sticker Star, bombs appear as stickers that are sometimes dropped by Bob-ombs. They can be used to attack enemies, however, the attack animation shows that Mario calls forth a Bob-omb to throw at them even though the stickers themselves are called bomb stickers.
Mario & Sonic series
The bombs seen in the Sonic series appear in Mario & Sonic at the Olympic Games and Mario & Sonic at the Olympic Winter Games. They are items in Dream Events that can be used by anyone. In Mario & Sonic at the Olympic Games, the player places them on the ground in Dream Race. Anyone who touches them is slowed down. In Mario & Sonic at the Olympic Winter Games, bombs go near the other players when used, and if they don't have a star, the bombs blow up and slow down the player. There is also a type of bomb called a bomb puck that is used only in Ice Hockey.
Mario & Luigi series
Mario & Luigi Dream Team
The bombs return in the tandem attack Bomb Derby. Using the Circle Pad, Luigi passes bombs to Mario who must hit them towards the enemy before the bombs explode. The last bomb is bigger and likewise does the most damage. These bombs are similar to Lemmy Koopa bombs.