Isolated and heavily fortified, Cobra Island is the prime headquarters of the evil Cobra organization. In some adaptations the island is shaped like the Cobra logo.
Marvel Comics continuity
Cobra's base was created by the machinations of Professor Appel, a Crimson Guardsman. Appell tricked the Joes into triggering a fault line beneath the Gulf of Mexico, resulting in a massive upthrust of the seabed. Despite a valiant effort, the Joes were unable to remove Cobra forces from the newly formed island. Cobra lawyers had secured the organization's recognition as a sovereign state from various governments, which resulted in the immediate withdrawal of the Joe forces from the island.
Devil's Due Comics continuity
The island was presumably destroyed by a nuclear strike at the end of the series.
In the Sunbow animated series, Cobra Island appears several times, but without much description as to its location, and with differing appearances. Its primary appearance matches that of the second season's opening credits: a swampy island covered with jungle terrain and several clear and low-lying areas. At the center of the island is the massive Cobra Terror Drome, which is situated atop a rocky cliff and converted into an inner sanctum for troops and vehicles that overlooks a long beach.
In G.I. Joe: The Movie the island is destroyed when the Terror Drome is infiltrated and destroyed by Sgt. Slaughter and his Renegades. Serpentor and the Cobra High Command survive in an underground bunker, which is all that survives the explosion. Cobra Island is presumably abandoned by Cobra following this event.