At the start, there will only be a few quests, but as you get to know the townsfolk better, more quests will be available.
All quests fall into one of three categories: general, simple, or battle. General requests have the greatest amount of variety and tend to be related to how well the main character has gotten to know the individual villagers. These sort of quests are also unique and are not repeatable. Simple requests are usually small tasks that can be repeated many times. Battle requests typically involve the eradication of problematic monster mobs and can also be repeated multiple times.
Some requests help the player to reach to the next boss. For example, in one of Daria's Request, completing the request will help the player to fix the broken bridge and then fight the Raccoon.
It is generally recommended to do as many quests as possible, as the rewards are plentiful and helpful for the player. Not to mention, quests are part of the marriage requirements. Each marriage candidate has 9 unique quests that must be finished before you can propose to her.
As with Rune Factory 2, the request board is back with a few tweaks this time.