This is an incomplete list of hideouts, bases, and headquarters in comics and animation. Such locations are a staple of the genre, and they are at times almost as iconic and well-recognized as the characters that own them.
Arrowcave - Former base of operations of the Green Arrow and Speedy. It was subsequently abandoned following Green Arrow's death. When Ollie went back to reclaim sentimental memorabilia, he found Solomon Grundy was living there.
Batcave - Batman's secret base of operations. Located under Wayne Manor and / or in the basement of the Wayne Foundation building. Contains a crime laboratory, computers and records, a host of weapons and space for numerous vehicles.
Dayton Manor - Headquarters of the Doom Patrol outside New York City.
Fortress of Solitude - Arctic fortress used by Superman as a secret lair. Created by a Kryptonian Relic called the Eradicator, the Fortress was a monument to Krypton on Earth. All of the items filling the Fortress were gathered from the otherworldly dimension known as the Phantom Zone (AOS #460).
Ha-Ha-Hacienda - Hideout of The Joker beginning in the early 1960s.
Justice Society Headquarters, formerly a brownstone building, which housed the JSA museum. Current version built by Lexcorp on the foundation of the former brownstone headquarters and museum. The former headquarters located in Gotham City, the latter in Manhattan.
The Lexcorp Towers complex, former headquarters of Lex Luthor. Located in Metropolis.
The Oblivion Bar, an extra-dimensional bar that only magically-talented persons can access. Headquarters of the Shadowpact.
Xavier Institute for Higher Learning (X-Mansion) - located at 1407 Graymalkin Lane in the town of Salem Center in New York State's Westchester County. Owned by Charles Xavier, aka Professor X, Xavier Mansion is the headquarters and training camp for both the X-Men and New Mutants. It contains two sub-basements which house the "Danger Room," laboratories, and an underground rail system that connects to the hangar facilities.
The Goblin House - a chamber inside of Oscorp that houses the Green Goblin's glider, armor, and arsenal of bombs that is secluded from everyone but the two Green Goblins, Norman and Harry Osborne.