There are loads of popular realms for each region. Japan has Chocobo, Tonberry and Masamune as far as my knowledge goes. US has Gilgamesh, Balmung, Leviathan, Hyperion, Excalibur and Sargatanas. And EU has Odin, Cerberus and Phoenix.
For example Balmung and Phoenix are known for Roleplay, Odin and Gilgamesh are known for raiding and Tonberry and Masamune are usually where the Australian playerbase goes. Basically those 2 Japanese ones are the unofficial JP English servers.