Bowser is currently ranked 29th on the current tier list. Bowser's moves have great range and strength, with all of his moves either dealing large amounts of damage, KOing his opponents early or generally putting his opponents in a disadvantageous position - most notably Whirling Fortress can very easily break shields. Bowser has an incredibly strong grab game - he possesses a combo throw in the form of up throw, his forward throw can KO opponents at high percents, his down throw can situationally chain grab and lead into some damaging follow-ups and his back throw can be used to position foes offstage and set up for an edgeguard. In addition to this, he possesses Flying Slam - a powerful command grab which can be used to equalize stocks via a sacrificial KO, and has a hitbox which can set up for some combos. Finally, Bowser has extremely powerful edgeguarding tools, with his forward air, back air and Fire Breath being especially powerful for edgeguarding and Bowser Bomb being able to punish opponents who do not sweetspot the ledge very powerfully.
However, Bowser suffers from having terrible mobility as he has the second worst dash speed in the game and a poor initial dash which gives him no reward for using the foxtrot or dash-boost techniques. This, alongside his mediocre frame data give him a poor neutral as his grab range is short and Fire Breath is not a reliable projectile. Furthermore, his disadvantage state is terrible - his combo breakers are not particularly reliable, his landing options are generally poor, leaving him vulnerable to characters with good juggling ability, and he is a large heavyweight, meaning he is very easy to combo. Finally, his offstage game is among one of the worst as his only reliable recovery special, Whirling Fortress, does not go very far at all and does not guard break very easily, meaning Bowser is easily gimped.
Whilst Bowser does have certain top players who use him, such as Gax and Miracle--7, Bowser's representation is not particularly spectacular due to the nerfs in patch 1.0.3 and the advent of Donkey Kong being a much more powerful character in the Metagame. Bowser's representation mostly revolves around him being used as a counterpick character for specific matchups.
Sweeps with his claws twice, first in front of him, then behind him.
In competitive play
Tier placement history
Bowser has been ranked 18 of B+ on the first Beta tier list due to taking down stocks easy from his brute strength, combo throw, and a decent kit. However in 18.104.22.168, Bowser has been significantly dropped due to his worst matchup's even more powerful and some nerfs like his running speed.
In v0.9b, there exists several files relating to Bowser, hinting that he was initially meant to be playable in an earlier build of the game. He has an unused announcer's call, two different variations of a character select portrait (one in the pre-v0.9 style), palette data, and is referenced numerous times in the character code.