Bowser (クッパ, Koopa), is the supreme leader of the Koopa Troop, and King of the Koopas. He is the main antagonist of the Mario series. Since his debut in the world-famous Super Mario Bros. for Nintendo Entertainment System as the archenemy of main hero Mario, Bowser is easily one of the most recognizable of all villain figures in the game industry. He has therefore appeared in Super Smash Bros. Melee, Super Smash Bros. Brawl, Super Smash Bros. 4, and Super Smash Bros. Ultimate in the Super Smash Bros. series as a playable fighter, and due to his size and strength, Giga Bowser (a gargantuan, power up version of said character), also appears in Melee as the final boss of Adventure Mode and as his Final Smash in Brawl, SSB4, and Ultimate.
Bowser was introduced in the seminal Super Mario Bros. for NES, with most of his traditional character traits introduced along with it: his storyline role as a comically monstrous villain who always goes out of his way to kidnap the Mushroom Kingdom princess, Peach Toadstool, his gameplay role as a boss enemy for Mario to defeat, his fire-breathing abilities, his immeasurable army of henchmen such as mushroom-headed Goombas and turtle-like Koopa Troopas, and so on. Super Mario Bros. holds the Guinness World Record for best-selling video game, at 40 million copies, essentially guaranteeing worldwide fame for all characters who appeared in the game, Bowser included. He has appeared in some form in almost every Mario game to date, along with more members of his "family," mainly his only child, Bowser Jr. and the seven Koopalings. He also has a helper named Kamek, who has raised him since he was born and serves as his mentor and father figure.
Bowser is a heavyset, chimeric, reptilian creature (officially described in Super Mario Odyssey as a "monster") who combines traits of various real and mythological animals. Like his Koopa Troopa underlings, he features elements of a turtle or tortoise (albeit with qualities of a fire-breathing dragon or dinosaur) with his shell and tail covered with spikes and the facial structure and horns of an ox, as well as a very distinctively-constructed face and red hair arranged like a mohawk, both very unlike a typical Koopa Troopa. To settle a common dispute original game developers intended for Bowser to be more of a dragon instead of his common perception as a turtle. Bowser, at times, is depicted in vastly different sizes, somewhat resembling Mario's tendency to grow or shrink in size during games starring him; he's a colossus in his appearance as the final boss of Super Mario Sunshine, while in other appearances he is only slightly larger than the average person.
Bowser is the primary villain in many Super Mario-themed platformers, and therefore usually not a playable character. Bowser has appeared as a playable character, however, in several Mario games nonetheless, such as in the Mario Kart series. Whereas Mario and Luigi are consistently the most balanced characters in the character line-up of any competitive Mario-themed game, Bowser traditionally fits the "big, slow, and strong character" archetype to the extreme in any game he is playable. In the various Mario-themed sports games, for example, Bowser performs relevant actions more powerfully than others but more slowly as well, while in the Mario Kart games, Bowser as a playable racer features the heaviest weight and the highest top speed of the racers, offset by low acceleration and handling abilities. This archetype is faithfully preserved in Bowser's appearance as a playable fighter in both Melee and Brawl. Yet despite this, Bowser's actual agility rating greatly varies in his of his appearances, especially in most competitive titles where he is playable in his home franchise, which is something more represented in Smash 4.
Bowser remains part of the regular cast in the Super Mario empire of video games, though his level of menace has fluctuated throughout his various game appearances. In many spinoffs, Bowser is on seemingly equal grounds with the other Super Mario characters in competitive games like sports and kart racing, and has even been helpful to the characters in some RPG roles - albeit typically to serve his own purposes. In particular, some of the RPG entries feature Bowser as a playable party member, even being a central protagonist in Mario & Luigi: Bowser's Inside Story. When in antagonistic roles, Bowser has occasionally been depicted as bumbling, comical, and almost slightly incompetent, but he works hard to come across as "bad" and supposedly has been doing so from a young age as Baby Bowser. However, most current Mario games return Bowser to his previous status of a legitimate threat, as can be seen in the transition from Super Mario Sunshine to Super Mario Galaxy and his character development throughout the Mario & Luigi RPG subseries. In such appearances, the Koopa King is more cunning and sinister than his brutish appearance would suggest, but is still boisterous, hammy and somewhat whimsical. Despite this, ever since the introduction of Bowser Jr. in Sunshine, one of Bowser's defining traits has been his love and support for his only son - regardless of how evil or competent either of them may be.
Bowser does not appear in the original Super Smash Bros. in any sort of capacity. However, according to a page on Smabura-Ken (the Japanese Super Smash Bros. site), Bowser was planned to be included as a playable character, but was cut. In fact, it has been confirmed that Bowser and King Dedede were actually playable characters during development of the game in 1998. In the end, Bowser would end up being completely scrapped while King Dedede became a background character in the Dream Land stage. This was mostly a result of the Nintendo 64's hardware limitations, as well as time constraints. The site held an official poll regarding characters for a potential sequel, and Bowser placed first with 169 votes. 
As a playable character
Main article: Bowser (SSBM)
Bowser makes his Smash Bros. series debut as a default playable character in the GameCube installment, and is billed as staying true to his archetype in normal competitive Mario games: he is among the heaviest and strongest characters in the game, but also among the most sluggish. Like Luigi, his appearance is based on his appearance in Mario Kart 64, except he has a noticeably more muscular frame and darker skin tones.
Bowser's neutral special move is Fire Breath, a continuous stream of fire breathed from his mouth into the area in front of him for several seconds until it weakens in power and size. His side special move, the Koopa Klaw, can be a good-range claw swipe attack, but can also grab onto enemies that are very close to him, and the move has the unique ability to grab onto enemies when both combatants are in midair. His up special move, the Whirling Fortress, is a third jump consisting of him withdrawing into his damaging spiked shell which is now spinning wildly upwards, and his down special move, the Bowser Bomb, causes a midair Bowser to crash down to earth vertically with great force. If Bowser is on the ground when doing this, he will leap up and in front of him diagonally before performing the crashing down maneuver.
Bowser's setup does not translate well in the fast-action world of Super Smash Bros. Melee. His powerful, damaging attacks with good range are good only when it manages to connect with opponents, for they have long wind-up and wind-down, and such a lack of alacrity seriously harms any fighter's ability to fight. His dash speed is slow, his jumping and landing animations are very laggy, and his wavedash is very slow and nearly useless. He is also not able to combo opponents, and his great size makes himself perhaps the easiest opponent to land combos on. Bowser players must therefore be able to read their opponents extremely well and must successfully pressure their opponents in battle, and make use of his good edge-guarding game, to have a chance at competitive play, though even an expert Bowser player will be severely disadvantaged against a regular Fox player.
Main article: List of SSBM trophies (Super Mario Bros. series)
Bowser is a playable character, so he is featured on three trophies that can be acquired by beating each Regular Match with him on any difficulty. His first trophy is earned by defeating the Classic mode as him on any difficulty, his second from the Adventure mode, and his third from the All-Star mode. There is also a trophy of Bowser at a younger age, "Baby Bowser", who is often confused with his son Bowser Jr..
Bowser's Classic trophy plays a large, symbolic role in Melee's "story", so to speak; the trophy is shown near the end of the opening FMV, getting struck by lightning. At the end of Adventure mode, after K.O.ing Bowser, the trophy is seen plummeting into the darkness. If the right conditions are fulfilled, however, the trophy will rise back up onto the stage, land, and get struck by that special lightning, which will cause it to break apart and reveal Giga Bowser breaking out of it, and the Giga Bowser battle begins. If Giga Bowser is defeated, the trophy will again be seen plummeting into the darkness, where it will now shatter like a little firework, signifying the player's ultimate victory.
Bowser's normal trophies read as follows:
As a playable character
Main article: Bowser (SSBB)
Bowser is another returning playable character in Brawl, but with an updated look with more realistic textures, though with a design more akin to the Mario series rather than his more muscular appearance in Melee. All but one of his special moves from Melee return in Brawl-- his side special move, Koopa Klaw has been replaced with a new move called Flying Slam. His appearance is based on his current appearance in the later Mario games, such as Luigi's Mansion, Super Mario Sunshine, Mario Party 4, Mario Kart: Double Dash!! and Super Mario Galaxy. As Masahiro Sakurai previously mentioned on the Smash Bros. DOJO!! website, Bowser now comes in a "slightly different flavor this time around", and like all the other characters; this can be taken as indication of Sakurai's claim that Brawl was designed with balance in mind.
Bowser's moveset and running speed are slightly faster than in Melee. His Forward Smash now has a chance to hit twice, once for the head, and again for his body, doing anywhere from 36 to 48 percent damage, and being by far, the most damaging smash attack in the game. While he has been buffed from Melee, Bowser is still a low tier character with the worst tournament results of any character in Brawl, ranking 33rd on the current tier list.
Main article: List of SSBB trophies (Super Mario Bros. series)
As a playable character
Main article: Bowser (SSB4)
Bowser returns as a playable character in SSB4, with a more upright posture and increased mobility. Like Mario, Luigi and Peach, his design is based on his appearance from recent Mario games, such as Super Mario 3D World and Mario Kart 8.
Bowser ranks 24th out of 55 characters on the tier list. He has been considerably buffed from Brawl to Smash 4, having been granted increased speed and faster attacks. The general changes to Smash 4 improve Bowser further, as he no longer has to contend with the likes of chain-grabbing, and the new rage mechanic brings more benefit to his great survivability. Yet, being a large and heavy character, he still suffers from combos and a lack of defensive options. Bowser has certainly improved from his past two appearances, and despite his small playerbase, he has achieved strong results.
Main article: List of SSB4 trophies (Super Mario Bros. series)
As a playable character
Main article: Bowser (SSBU)
Bowser returns as a playable character alongside the entire playable roster of the series. This is Bowser's first appearance in Super Smash Bros. where he is not a starting character. As the first character in Donkey Kong's unlock tree, he can potentially be the first character to be unlocked.