Individuals, shops, or organizations will request your aid from time to time --- and you may accept or decline as you wish. The conditions for most quests are fairly loose, and typically do not require you to have a specific job level, ability, or allegiance. Quests rarely result in worthwhile monetary gain, but they do increase your characters Fame in the area where you complete the quest. Certain quests, like unlocking an Advanced Job, will require a certain level of fame. Fame represents the amount of trust the NPC's in the area have in a you. Fame also slightly influences the prices from NPC merchants in the area -- higher fame results in lower prices.
Starting Nation Quests
Treasures of Aht Urhgan Quests
Notorious Monster Quests