Californian island prison, operational 1859-1936.
With the number of costumed and super-powered criminals coming to the fore in the late 20th century a number of them were incarcerated at Alcatraz. In 1941, it was where Human Torch foe the Parrot was incarcerated until he escaped and was subsequently slain by his foe. It was also where Nazi assassin the Python was incarcerated before he was broken out of prison on orders from Hitler himself. The Human Torch, Toro and Sub-Mariner attempted to stop the escape, but failed. They eventually slew the Python in New York City.
Two prisoners on Alcatraz escape their prison cell using a magical Monkey's Paw taking them on a journey through time. They first they arrived on the RMS Titanic, then the Hindenburg and finally ending up in Hiroshima, just before the Atomic Bombings of Hiroshima and Nagasaki.
Given the threat posed by the Beyonder, Rachel Summers decided to kill him. She found him on Alcatraz Island and attacked with the full power of the Phoenix force, resulting in a huge explosion, yet he made it so that she barely did any damage and then transported the two of them away.
When the X-Men relocated to San Francisco, Cyclops briefly used Alcatraz Island to meet secretly with the members of X-Force. Around the same time, Ikaris teamed up with the X-Men to battle Druig's team of Eternals on the island.
Alcatraz Island later served as H.A.M.M.E.R. West for Norman Osborn's Dark Avengers and Dark X-Men. The island housed Omega Machine and the served as a detention center for captured mutants. Their ambiant power was also used to fuel the Omega Machine and Weapon Omega. Dark Beast also experimented on his mutant prisoners.
After the World War Hate, when Tony Stark's moral compass was magically inverted, he moved to San Francisco, and made of Alcatraz his new headquarters: Stark Island. Stark's building was heavily damaged by an army of Iron Man Armor controlled by a digital back-up of Stark's mind, which retained Tony's original personality and antagonized his creator in order to try to get him back to his normal self.
Ever since Stark moved back to New York, Alcatraz returned to its regular appearance, and eventually became the terminal of a surveillance network created by the Owl, though it was subsequently taken over by the Shroud in order to find his ex-lover, Madame Web. After the Shroud's was locked up, Madame Web used Alcatraz Island as a base of operations and put the Owl's equipment to use in order to investigate New U Technologies.
When Hydra took over the United States and displaced mutantkind to California, turning it into the Sovereign Republic of New Tian, Alcatraz was reopened as a detainment center, used to imprison all those that opposed Xorn's regime.
X-Men Cinematic Universe (Earth-10005)
When Magneto was leading his Brotherhood of Mutants to overtaken Alcatraz and destroy The Cure, he moved the entire Golden Gate Bridge as passage to for his army. It was here that the X-Men had their last stand against Phoenix and the Brotherhood.
Alcatraz island was a prison for dangerous mutants. Governor Harcourt Teesdale (AKA Arcade) served as the director-governor. He created mutant-themed attractions to tortures and punish prisoners. A mutant named the Basilisk was used as an unwilling executioner for years until we was able to escaped, murder Arcade, and free the mutants imprisoned there.