Volcano Lair

Some people want to live not at volcano's feet, but in a volcano. Whether it's active or extinct. After all, a crater inside some big mountain is a relatively defensible location, it looks impressive and Everything's Cooler With Lava. Usually Supervillain Lair, but not always. Naturally predisposed to become a Collapsing Lair.

Most feature labyrintine cave complex, Lava Pits and use of free heat. Often done in a rather careless manner. May or may not be located on an island.

Anime and Manga

 * Great Mazinger: Marquis Janus, one of the villains of the Mazinger Z sequel had an Island Base with an artificial volcano built on the center. Its eruptions could be set off and stopped at will. Often it was used to blast Great Mazinger with a rain of hot-molten rocks, debris and volcanic cinders in order to slow down its advance or hinder The Hero Tetsuya as he battled.
 * Kotetsu Jeeg: Queen Himika's Home Base was inside a volcano.
 * Starscream's temporary base in Transformers Cybertron is located on a volcanic island in the Pacific. Since he and his minions are giant alien robots, the heat is not an issue. Hell, Thunderblast enjoys bathing in the lava.

Film

 * Austin Powers—Dr Evil's Island Base
 * Disney version of 20,000 Leagues Under the Sea—Captain Nemo's island
 * Spy Kids 2 (Island Base)
 * You Only Live Twice—Blofeld

Films -- Animation

 * The Incredibles—Syndrome's base at Nomanisan Island.

Literature

 * Dragonriders of Pern has all "classic" Weyrs made this way (one of the rare occurrences of this trope with extinct volcanoes,) but not early or later ones.
 * Evil Harry Dread, the low-budget Evil Overlord in The Last Hero, complains that other Dark Lords somehow manage to get volcano lairs even when the local geology is completely wrong for them.
 * The Cosmic Computer by H. Beam Piper includes a gang of bandits who've taken over an abandoned spaceport built into an extinct volcano. The port was constructed during a war, and it's well armed for defense -- not to mention that when it was abandoned, a lot of its manufacturing and repair equipment was left behind....

Live Action

 * The villain Moltor of Power Rangers Operation Overdrive bases his operations inside one of these, in sharp contrast to his brother Flurious, who resides inside of an icy cave lair.

Tabletop RPG

 * Dungeons and Dragons
 * Dragonlance—The biggest Minoi settlement around is Mount Nevermind. A combination of their smokepowder storage facility and one angry red dragon led to reactivation of the volcano and subsequent discovery of useable geothermal energy.
 * Forgotten Realms—Firenewts live in volcanic mountains. Because they need Lava Pit-grade heat.
 * Red dragons, being immune to fire, prefer hot lairs including volcanoes.

Video Games

 * Boiling Point: Road to Hell
 * Evil Genius
 * Far Cry
 * Kingdom of Loathing
 * Red Alert 3
 * Subverted in No One Lives Forever 2. It looks like this but, as it turns out, the actual lava pit inside the base would be too troublesome—so the villains use synthetic lava instead.
 * MARDEK has at least one NPC who lives in a volcano, a mad hermit.
 * Mega Man's Dr. Wily had a couple, with at least two in the Mega Man Battle Network series.
 * In the Super Mario Bros. series games, Bowser's castle is usually found inside a volcano. In Super Mario Galaxy, Bowser's castle is instead orbiting the Sun, and in Super Mario Galaxy 2, it's near a black hole.
 * from Pokémon Mystery Dungeon: Explorers of Time/Darkness/Sky.
 * Pokémon Emerald: Team Magma's headquarters is located in Mount Chimney, specifically because that's where Groudon is.
 * The Elder Scrolls:Morrowind has the Big Bad's Very Definitely Final Dungeon in the crater of a volcano.

Web Comics
"Minion No. 1: I totally told you, WE LIVE IN A VOLCANO! There's NO SUCH THING as a "minor plumbing problem"!"
 * Minions At Work as a comic about going-on in Supervillain Lairs featured volcanic lair of Doctor Coldblood time and again, with lots of jokes about its volcano nature.

"After all, nothing quite says "intelligent" like having 70 billion dollars of equipment next to an unstable volcano!"
 * The Original Gobwin Knob in Erfworld was built on an extinct volcano.
 * Dan and Mab's Furry Adventures lampshaded this with Dr. Jyrras explaining why he specifically chose an extinct volcano for his Island Base:

Web Original

 * Villain Source—volcano Island Base

Western Animation

 * In the My Little Pony TV show and movie, witches lived in the Volcano of Gloom.