Hidden in each of the regions are side quest which can be found by looking for characters that have a text box above their heads with a red exclamation mark. Not all the side quests will be immediately available as several can be found in major towns after the completion of a dungeon.
Dueling Peaks Sidequests
Misko, the Great Bandit
Quest Giver: Domidak and Prissen, Dueling Peaks Stable
Reward: 50 Rupees
Wild Horses
Quest Giver: Rensa, Dueling Peaks Stable
Reward: 50 Rupees
The Priceless Maracas
Quest Giver: Hestu, on your way to Kakariko Village
Reward: Inventory expansion
Koko's Culinary Quest
Quest Giver: Koko, outside the Kakariko Village General Store
Reward: Food items
Flown the Coop
Quest Giver: Cado, opposite the Kakariko Village Armor Shop
Reward: 50 Rupees
Arrows of Burning Heat
Quest Giver: Rola, Kakariko Village General Store
Reward: 20 Rupees
Playtime with Cottla
Quest Giver: Cottla, around Kakariko Village Armor Shop
Reward: Rock Salt
Find the Fairy Fountain
Quest Giver: Pikango, Kakariko Village
Reward: Hints
By Firefly's Light
Quest Giver: Lasli, Kakariko Village
Reward: 50 Rupees
Hateno Sidequests
The Statue's Bargain
Quest Giver: Teebo, Hateno Village
Reward: Ability to swap Spirit Orb rewards
The Weapon Connoisseur
Quest Giver: Nebb, Hateno Village
Reward: Up to 1140 Rupees (or equivalent in gemstones)
A Gift For My Beloved
Quest Giver: Manny, Hateno Village near Inn
Reward: 100 Rupees
Hylian Homeowner
Quest Giver: Bolson, Hateno Village
Reward: Your very own house!
The Sheep Rustlers
Quest Giver: Koyin, Hateno Farm
Reward: 10 Bottles of Fresh Milk
Robbie's Research
Quest Giver: Purah, Hateno Ancient Tech Lab
Reward: 3x Ancient Arrows
Slated for Upgrades
Quest Giver: Purah, Hateno Ancient Tech Lab
Reward: Rune upgrades
Sunshroom Sensing
Quest Giver: Symin, Hateno Ancient Tech Lab
Reward: 3x Hearty Truffles
The Hero's Cache
Quest Giver: Kass, Kitano Bay
Reward: 300 Rupees
Lanayru Sidequests
Lynel Safari
Quest Giver: Laftlat, by Zora's Domain Throne Room stairs
Reward: Zora Greaves
Diving is Beauty!
Quest Giver: Gruve, by Zora's Domain Throne Room stairs
Reward: 5x Fleet-Lotus Seeds
Frog Catching
Quest Giver: Tumbo, by Ne'ez Yohma Shrine
Reward: Armoranth
The Giant of Ralis Pond
Quest Giver: Torfeau, under Zora's Domain Throne Room
Reward: 100 Rupees
Zora Stone Monuments
Quest Giver: Jiahto, under Zora's Domain Throne Room
Reward: Diamond
A Wife Washed Away
Quest Giver: Fronk, near Zora's Domain General Store
Reward: 5 Staminoka Basses
Luminous Stone Gathering
Quest Giver: Ledo, Zora's Domain Plaza
Reward: Up to 2 diamonds per stone
Special Delivery
Quest Giver: Finley, Bank of Wishes
Reward: 300 Rupees