Goron Quest
The Goron Quest has three rewards to it. One being a Bottle, another being getting the Goron Merchant to come to Hyrule Town Square, and the other being the series of events that lead to getting the Mirror Shield (see above for details).
[1] Find the Goron in southwest Lon Lon Ranch, who you can reach by using the various vortices and Ezlo ability to act as a parachute. Fuse Kinstones with the Goron and his buddy, the Goron Merchant, will arrive in Hyrule Town.
[2] Now, the Goron will return to punch the wall without result. Clearly, he needs a boost. To help him out you need to track down five "Mysterious Walls" and fuse with them, to make five Gorons appear to slowly help the original Goron make his way through the cave (to the delicious rocks at its end). You can find the five Mysterious Walls hidden in diggable caves (accessible using the Mole Mitts).
[3] But first, go to Eenie and Meenie's farm in Eastern Hills. To get there, just head south of where the Goron is, and west in the next screen. Fuse Kinstones with Eenie (to the top one) and the Goron will punch through the wall and into the cave beyond. Now, you can begin recruiting. The Mysterious Wall caves are located as follows:
[Eastern Hills] At Eenie and Meenie's farm, just north of the two, is a cave.
[Minish Woods] In the same area as Syrup the With's house, there is a cave just south of the stairs leading to her hut.
[Trilby Highlands] Right before the bridge that leads to Mt. Crenel is a bridge going north. Cross it to find a cave.
[Mt. Crenel] Next to the Hermit's cave, all the way up the Crenel Wall, is the cave you seek.
[Lake Hylia] From the dock south of Stockwell's lake House, jump from island to island in the Lake, which leads up to the cave.
[4] Return to the Goron Cave where the Gorons will have punched through all the way to the end. Inside you can find the Bottle and 200 Rupees in a chest. Also, you can fuse with the rightmost Goron to wake Biggoron at Veil Falls.
Dampe's Grove
After opening up the Royal Crypt, talk to Dampe and he'll be muttering a series of directions for the Lost Woods. Go there, and go Left three times, and Up three times to find a hidden grove. There open the chest to grab 200 Mysterious Shells from the contents.
Dungeon Simulation Game
After the Fortress of Winds, the house with the Ghost on top will be open for business in Hyrule Town. Inside is Simon's Dungeon Simulation Game, which involves you being dropped in a large arena filled with monsters. Initially it's just Helmasaurs, Charger Turtles, and Ropes. Once you complete that, a new crew appears, including Stalfos, Bomb-ombs, and Grey ChuChus. When you defeat the second round, a chest appears with a Heart Piece inside. Also, the little scene when you wake up from the simulation is hi-larious!
Find Houses for the Oracles!
After the Fortress of Winds, the Inn will finally open in Hyrule Town. Inside you can find the three Oracles (from the Oracles series), who are looking for homes. Fuse Kinstones with Farore (the green one) and Gorman will arrive in town. Rush over to talk to him and he'll explain his dire situation: he needs to rent his house out, but will only do so to a single female (the creep). Run back to the Oracles and offer the house to one of them. I suggest Farore, for reasons I will explain momentarily. Next, run over to the Post Office and fuse kinstones with Bremor (who's holding a 2x4), and Mutoh will begin building a house just south of the Post Office. When it's complete (enter and exit a building three times to finish it) you can offer it to another Oracle.
Now, what is the point of all this? Well, when an Oracle is housed, you can then talk to her to get a Charm, which depending on the Oracle will buff a particular aspect of yours. Nayru's Charm will boost your defense, Din's your strength, and Farore's will boost both 9making Farore the ideal choice!).
Joy Butterflys
After the Royal Crypt, you can fuse Kinstones with each of the three Oracles. By fusing with each, a Joy Butterfly will appear in one of three different places. Catch it to gain a boost to your abilities!
[Nayru] The Joy Butterfly will appear in the Graveyard. Catching it will allow you to swim much faster.
[Din] The Joy Butterfly will appear in the Wind Ruins. Catching it will allow you to shoot arrows much faster than before.
[Farore] The Joy Butterfly will appear in Castor Wilds. Catching it will allow you to dig much faster than before using the Mole Mitts.
Beedle
After the first dungeon you'll spot a good deal of dust on the rug next to the fruit vendor. Use the Gust Jar to remove it and return later to find that Beedle has set up shop. The fellow sells Picolyte, which you can use to find certain objects. As handy as this may seem, for the price, it is quite worthless. I advise avoiding the use of this moneysink, but that's just me.
Infinite Rupees?
Outside Link's house, dig around the left side of the "yard" to eventually uncover a shiny Red Rupee. Go inside the house and back outside to do it again. You can repeat this ad nauseum for "infinite" Rupees.