Bark the Polar Bear

Bark the Polar Bear debuted in Sonic the Fighters, an arcade game featuring Sonic characters.

Sonic the Fighters
In Sonic the Fighters Bark had been entrusted with one of the Chaos Emeralds to prevent Dr. Eggman from abusing it. When the Death Egg II appeared, Bark and other Chaos Emerald Guardians gathered to see who was the strongest and thus best option to travel there in Tails' single seat spacecraft to destroy Eggman's creation.

Bark is a pure powerhouse character who sacrifices speed for overwhelming strength, hitting harder than even Knuckles in this game.

Fighters Megamix
Bark later showed up with Bean the Dynamite in Fighters Megamix, a crossover fighter which had him set against the casts of Virtua Fighter 2 and Fighting Vipers as well as Janet Marshall from Virtua Cop, Rent-a-Hero's Taro Yamada and a bizarre bunch of other fighters such as 'Kid' versions of Akira Yuki and Sarah Bryant, Hornet from Daytona USA (a car), Mr. Meat(quite literally a floating meat on the bone with floating hands and feet), Deku (a strange anthromorphic mexican green bean) and Sega AM2's Palm Tree logo.

Sonic Generations
After this title Bark, alongside Bean the Dynamite, went missing from games although according to a wanted poster cameo in Sonic Generations they appear to be considered 'armed and dangerous' and are partners of sorts. It is unclear if this wanted poster is from G.U.N., Dr. Eggman or just the police of City Escape.

Sonic Mania
Whilst Bark himself doesn't appear in Sonic Mania, his likeness does via an illusion created by Heavy Magician, a badnik member of the Hard Boiled Heavies. In this game he, Bean and Fang the Sniper appear to be standing on badniks as the Tornado is taken down, and are later used by Heavy Magician to fight off Sonic, Tails, Knuckles, Mighty and Ray.

The Bark illusion slowly hops around the stage, smashing his fists down into the ground with pure power causing ceiling elements (like fan pieces and ceiling tiles) to come crashing down on the heroes.

Ultimately the Bark illusion is defeated by the heroes.

Sonic the Hedgehog (Archie Comics)
Whilst Bark is portrayed more as a heroic character in Sonic the Fighters, the Archie comics have him as a criminal partner to Bean the Dynamite and later Fang the Sniper as part of a mercenary trio.

The Archie comics portray Bark as being a silent but powerful force to be reckoned with, although he is not without honor and is said to have some good in him. He is also a lot smarter than he first appears despite his ferocious nature.

Trivia

 * Bark makes a cameo appearance alongside all the other playable fighters from Sonic the Fighters in both Shenmue and Shenmue II as a capsule toy for Ryo Hazuki to collect. Due to Yu Suzuki's split from Sega, Shenmue III does not have Bark return as a capsule toy.
 * There is an official plush toy of Bark that was only ever released in Japan. It was winnable from claw machines. This is one of the few official pieces of Sonic merchandise to be based on Bark.