You can't go wrong with Rodan; he's just classic. His first appearance was actually in his own movie, Rodan, after which he teamed up with Godzilla and Mothra to fight King Ghidorah in Ghidrah, the Three-Headed Monster. Since then he has been a constant presence in the franchise. A very simple monster; Rodan is a large species of prehistoric pteranodon. He's had a complex relationship with Godzilla over the years; often switching between being friend or foe. Rodan's most powerful ability is his supersonic speed. He is able to fly at speeds of Mach 1.5, which, needless to say, can cause untold amounts of damage to any surrounding structures. All Rodan need do is fly over a city and the wind generated from this intense speed with devastate everything in his path. He can also use this ability to hold his foes at bay and keep them off their feet. When he was re-imagined in the Heisei series of films, he was given a substantial power boost in the form of a heat beam. Rodan may not have as much going on aesthetically as some other monsters of the Godzilla series, but he is so ingrained into the mythology of Toho's monster movies that he remains one of the most popular and significant. There is a reason so many people thought Rodan would be in the new movie. Rodan is classic Godzilla.