Included with the 1988/89 NES game Godzilla: Monster of Monsters was an ad for a game simply titled Rodan, based on the Pteranodon-like flying monster (once a star of his own film and later one of Godzilla's foes/allies). It was also briefly mentioned in several magazines, such as issue 16 of Nintendo Power, as well as the September 1990 issue of GamePro, and was said to be a direct sequel to Godzilla: Monster of Monsters.
The game was merely cited as featuring "Rodan, Godzilla's arch enemy", even though this isn't quite accurate (King Ghidorah being closer to that). It was advertised as "coming 1991", but the game never emerged and the ad was never followed up on. Rodan did, however, appear in what became the actual Godzilla NES sequel, Godzilla 2: War of the Monsters. Neither the fate of the unfinished game, nor its level of completion have ever been made public knowledge.
On a somewhat related note, a Rodan figure was produced for the 1970's Shogun Warriors line, a companion piece to the claw-firing Godzilla, but in much smaller numbers, making it effectively almost as rare as the game that was never released.