ALTERNATE VERSIONS
Hank McCoy took a high risk when he drank the mutagenic serum he had, and his counterpart of the alternate timeline depicted in What if (1st series) #37 was not as lucky as him. This Hank had concocted a more concentrated serum and, when he drank it, his mind was also affected by his transformation. No longer the bright intellect, the Beast strolled the back alleys of New York to search the trash bins for food. When he was approached by the X-Men, Hank recognized them as his old friends but, perceiving their attempts to help than as an attack, he fought back with all he had. Almost killing the Angel and Marvel Girl snapped him back to his senses, though the Beast knew that he couldn’t keeps his animalistic instincts for too long and urged Professor Xavier to help him. The ultimate solution was found when the X-Men relocated the Beast to the Savage Land, where their friend, Ka-Zar, would keep an eye on him.
While sent away in one reality, in another one, shown in What if (2nd series) #9, Hank was the only X-Man left. Both old and new members of the X-Men having perished in their battle against Krakoa, Professor Xavier blamed himself and a concerned Hank quit the Avengers to take care of his former mentor. As Xavier’s state of depression didn’t improve, Hank asked the Professor’s former love, Moira MacTaggert, to visit the Professor, and she brought along her young ward, Rahne Sinclair. Just like in the main universe, Count Nefaria soon threatened the world and, with all other hero teams unavailable, Beast had to use Cerebro to contact several mutants from all over the world and teleport them to Nefaria. Despite them being untrained, the mutants defeated Nefaria’s Ani-Men, and most of them stayed around to become part of the newly-formed X-Men, now led by the Beast.
The Age of Apocalypse version of the Beast grew up in a very harsh environment, shaped by Apocalypse’s law of survival of the fittest. Hank McCoy was the Dark Beast of Apocalypse's labs, so named by the inmates of the pens whom he frequently used as test subjects. McCoy possibly even matched Sinister for unscrupulous experimentation in the name of science. Unlike McCoy from Earth 616, the AoA's Beast knowingly subjected himself to his bestial transformation, becoming bigger and stronger in the process, and apparently not minding the fangs and gray fur that came along. When the X-Men attacked Apocalypse’s citadel, McCoy learned of their plan to go back in time and alter the timeline, so he secretly followed them, ending up ca. 20 years in the past of the Earth 616 timeline. Though his memory was somewhat jumbled, this was easily fixed during an encounter with a very young Emma Frost and, in the years that followed, the Dark Beast built himself a base of operations in the sewer system beneath New York, where he also had a hand in engineering the Morlocks. Staying hidden for the better part of two decades, McCoy eventually started to become directly involved, like for example when he further kidnapped the “real” McCoy and further altered his own looks to take the Beast’s place among the X-Men, or later on when he became a lackey of Onslaught.
The Dark Beast was one of the few to retain his powers when the Scarlet Witch depowered around 99% of the world’s mutant population. He set out trying to discover a way to restore the mutant X-gene and ended up joining the 616 universe’s Beast in his endeavors. Whilst Beast still kept hold of his ethics, Dark Beast wasn’t so strict and he intentionally placed children in danger as part of his investigation. A while later, he got a chance to return to his home universe thanks to Wolverine’s X-Force and, when he arrived there, he found it had succumb to even more devastation after he had left. He returned to Earth 616 again but his thoughts often strayed back to his home reality. 
Eventually, he recruited his own universe’s Nightcrawler into helping him get back home. The portal they created between the worlds didn’t close like it was supposed to and they accidentally unleashed an army of monsters that threatened all of reality. In the end, the X-Men evacuated him back to the main universe and his home reality was closed off, seemingly forever.
McCoy laid low for a while, instead chosing to work from the shadows to stir up trouble between SHIELD and the X-Men. He even infected some of the X-Men with nanites, disrupting their powers. McCoy's plans were eventually discovered but by that point he had sparked an all out war between the two groups. In the final showdown he was seemingly killed by a bomb he had planted in his suit. McCoy was revived by Sinister as a cybernetic organism with numerous integrated mechanical parts.
After X-Man wiped out most of the X-Men, Dark Beast was captured and forced to work for Cyclops's remaining team. Despite being an evil sadistic bastard, McCoy enjoyed the scientific puzzles Cyclops placed before him, such as curing the New Mutants of their techno-organic infection. When McCoy developed an anti-vaccine to prevent humans from using the mutant vaccine to eliminate mutations in children, the X-Men trusted him and released the bio-agent into the atmosphere. In fact, McCoy's solution caused a dangerous reaction in mutant children injected with the vaccine, causing them to mutate uncontrollably and fall into comas, thus making the mutant vaccine too dangerous to use. When the X-Men found out, Magik was furious and severed McCoy's head with her stepping disk portals.
When Morgan le Fay used the Twilight Sword to reconstruct reality to her whims, the entire world was blasted back to medieval times. She kept the Avengers, who had opposed her, around as her personal royal guard, the Queen's Vengeance. Beast was recreated as Kreature, a near-mindless beast apparently filled with violent rage and with no vocabulary beyond gutteral snarls and yelps.
Fortunately, some Avengers remembered that this was not how the world was supposed to be and eventually the Scarlet Witch could use her teammates‘ united energies to disrupt Morgan’s spell and reality was restored [Avengers (3rd series) #2-3].
In the Mutant X Universe, Hank McCoy's experiments on himself ended even worse than in ours. Becoming the Brute, Hank gained amphibious skills but lost nearly all his intelligence in the process. He was further mutated by the demons during Inferno, giving him cloven hooves for feet. As a side effect of his changes, the Brute also possessed a berserker streak, rivaling Wolverine. When pressed, he could be frighteningly lethal to his opponents, though most of the times his mood was that of a naive child. When Havok left Magneto’s X-Men, he took the Brute and several other members along, to form their own superhero team, the Six. 
Years later, Hank briefly regained his intelligence as an after-effect of a severe mindblast by the villainous Charles Xavier. However, instead of trying to stabilize this condition, Hank devoted his short time of clarity to help his teammate, Ice-Man, to dampen down his powers somewhat, so that he could transform back to flesh-and-blood from the iceform he had been trapped in for years. Right after the treatment was finished, Hank reverted back to his mentally handicapped level.
When the Inhumans’ Terrigen Mists were accidentally released into the atmosphere in the alternate timeline dubbed Earth X, every human being on Earth gained superpowers and mutants were no longer outcasts. The world no longer in need of heroes, Hank turned to science again and, over the years, as he got older, his fur turned white. At the request of King T'Challa and Queen Ororo, he was living in Wakanda, partially to study the nation’s evolved animals, who had become humanoid and were capable of speech.
At first, it seemed that they had been affected by the Terrigen Mists as well but, while Hank helped transporting Wakanda's royal family and the Ani-Men from frozen Africa to safe haven in the Savage Land, he discovered that their transformations had been caused by the Cosmic Cube that Captain America had left in T’Challa’s care. The truth revealed, T’Challa handed the Cube over to Captain Marvel for his attempt to defeat Death. However, once the heroes realized that without Death people could no longer die, not even the ones suffering from mortal injuries, the Beast returned to civilization to help other scientific geniuses to create a replacement for her.
In the Ultimate universe, Hank McCoy was a brilliant young man, whose physical mutation was obvious, which is why he was kicked out of his parents' home during an anti-mutant craze. A short time later, he was found by Jean Grey, who recruited him for the X-Men. While his genius made him a seminal team member, Hank was always insecure because of his looks and couldn’t really fathom that someone as beautiful as Storm would fall for him. These feelings deepened when, due to the experimentation on him by Weapon X, he became blue and furry. Hank’s insecurity regarding his relationship increased when a new teammate, the handsome Angel, was clearly attracted to Storm. Hank left the team, only to be invited into Emma Frost’s team of media-friendly mutants chosen by the US president. When this team was introduced to the public, Sentinels attacked. Hank bravely tried to save lives and perished in the attempt, as he was hit by falling debris. His death proved traumatic for his former teammates, especially Storm.
Eventually, the X-Men were shocked to discover that Beast hadn’t died like they thought, and it was in fact Xavier who had fooled them into thinking he had. Instead, the Beast had been taken away by the government and given a top secret project of finding a cure for the Legacy virus.
Professor Xavier had used his powers into making Hank believe he was staying in contact with his friends and family the whole time. However, when Xavier was killed, the effects wore off and Hank realized what had really happened. Hank eventually rejoined the X-Men but would soon be killed for real when Magneto unleashed an enormous tidal wave on New York.
A time-traveling experiment gone wrong created another divergent timeline, one in which present day heroes already emerged in the 17th century, the year 1602 to be precise. Mutants were referred to as “witchbreed” and, as such, feared and hunted. The counterpart of the Beast too was named Hank McCoy, though his history is somewhat different. While not in his furry form, Henry didn’t pass for a regular human either, too grotesque was his physique. His mother was often accused of having mated with an ape to have such a child and it was too much for her to bear. She died and Henry’s father followed her not much later. Henry McCoy lived on his own for a while, until he was taken in by Carlos Javier.
After the newest X-Man, Xorn, was revealed to have been “Magneto“ in disguise and had killed Jean Grey, Xavier abandoned the school and Cyclops was about to follow, feeling guilty over his affair with Emmy Frost. Being the only one to stay behind, Hank fought tooth and nail to keep the Xavier Institute open, but ultimately he wasn’t wasn't capable of handling all the responsibility that had been thrust on him, and he began taking the drug Kick to cope with the pressure. As a result, Hank became the new host body for Sublime, the sentient microscopic lifeform who existed in aerosol form within Kick. 150 years later, the still-possessed Hank McCoy was battling the few surviving X-Men and their new and old allies, using his legions of artificially-engineered Crawlers and his pointman, Apollyon. Gaining possession of the Phoenix Egg, Beast-Sublime managed to convince the nascent, reawakening Jean Grey to fight on his side. Before it was all over, however, Jean Grey regained her full memories and halted the spread of the cancerous timeline. As she passed on to another plane of existence, Phoenix reached a century-and-a-half back in time to give Cyclops a “push“ to get over her death and accept Emma Frost’s offer to become co-headmasters of the new school. As such, the events that led to Beast's downfall and corruption were prevented [New X-Men (1st series) #151-154].
When Legion warped reality to create the Age of X, he incorporated everyone who was on Utopia until his world. As Beast had left the X-Men at that point, his absence was explained in the world due to him being dragged out of him home and beaten to death by anti-mutant protestors years before.