Increased Deku Nuts 1: Go R,L,R,L,F,L in the Lost Woods and bomb the rock there. Fall down and beat the first shrub guy and pay him 40 rupees to get the upgrade to 30 Deku Nut capacity.
Increased Deku Nuts 2: Go R,L,R,L,L in the Lost Woods and fall down the hole in the grass near the butterflies. Wear the Mask of Truth and be judged. The shrubs will decide that you are ugly but give you the Deku Nut upgrade to 40 Deku Nuts anyway. There is a bug in the game that makes it so you can't get this after a certain point (which isn't yet known, but believed to be once you first become adult Link). So you want to do it the second you get the Mask of Truth, and thus want to get the Mask of Truth as soon as you can (immediately after getting the Ocarina of Time).
Increased Deku Seeds 1: Go to the Lost Woods. Go right from the first room and you'll see a round gray object hanging from a tree. Hit it with your slingshot. Get three bullseye's in a row (100 points is a bullseye) and you'll get a bigger Deku Seed bag that holds 40 Deku seeds.
Increased Deku Seeds 2: In the market is a target shooting game. Hit all the targets to increase your Deku seed carrying capacity to 50 seeds.
Increased Deku Sticks 1: Go to the Lost Woods. Go left from the first room and then go on to the next room after that. Walk across the room to the ramp on the other end, and one of those bush monsters will be there. Knock it out by deflecting its bullet back to it and it will ask you for 40 rupees. Pay the 40 rupees and you'll get a 20 Deku Stick carrying capacity.
Increased Deku Sticks 2: Borrow a Skull Mask from the Happy Mask Shop as young Link. Go to the Lost Woods and go R,L,R,L,L. Walk in the grass in the back of this area near a bunch of butterflies until you fall down a secret hole. Immediately put on your skull mask and walk forward. All these little guys will start hopping around you. Make your way to the right to a bush monster that's still submerged in the ground and talk to him to get a 30 Deku Stick carrying capacity. You can also wear other masks in this area to get other prizes.
Increased Bombs 1: In Goron City there is a wild rolling Goron on the 3rd floor. Stop him from rolling while he's in the tunnel by using a bomb. He'll give you a Big Bomb Bag which allows you to carry 30 bombs.
Increased Bombs 2: One of the random prizes in the Bombchu Bowling game is a bigger Bomb Bag which allows you to hold 40 bombs.
Increased Arrows 1: You can get a bigger quiver (40 arrow capacity) by playing the Shooting Gallery in Kakariko Village.