Haven't seen this posted yet, so thought I'd share. These are from multiple unofficial sources, but many people are corroborating the info so I'm calling it 95% accurate. This is just the requirements to unlock the job, does not count other classes' skills that can be used by the job.
Bard = 30 Archer / 15 Pugilist
Summoner = 30 Arcanist / 15 Thaumaturge
Scholar = 30 Arcanist / 15 Conjurer
Dragoon = 30 Lancer / 15 Marauder
Black Mage = 30 Thaumaturge / 15 Archer
White Mage = 30 Conjurer / 15 Arcanist
Monk = 30 Pugilist / 15 Lancer
Warrior = 30 Marauder / 15 Gladiator
Paladin = 30 Gladiator / 15 Conjurer
from http://www.reddit.com/r/ffxiv/comments/1l29jn/all_job_requirements/