It's possible to complete every dungeon in the game without ever obtaining any of the strength upgrades: The Goron Bracelet, Silver Gauntlets, and the Golden Gauntlets.
And since this skips one of the two places you'll ever need Saria's Song, we'll show you how to do that as well.
The most important item required for skipping the strength upgrades are Bombchus. You can get them early from either the Bottom of the Well or the child Spirit Temple.
Once you get Bombchus, you can simply use one to blow up the boulder blocking it. Inside DC just use chus for anywhere you would normally need to use a bomb flower until you obtain bombs normally. Once you get bombs you're fine until the adult portion of the game.
When traveling to the Forest Temple as an Adult, Mido block your path to the Sacred Forest Meadow unless you play Saria's Song. However, can use a well-angled backflip to jump over him. To backflip right next to Mido without talking to him press C-up first, then press A twice in succession to close C-up mode and backflip on the frame after.
You can also get over him with a megaflip which is slightly faster if done well.
A lesser known fact about the Goron Bracelet is that even as an Adult, the bracelet is still required to lift bushes objects and push large blocks.
See Forest Temple - Block Room Speed Trick for more information.
Like the Forest Temple, there is also a block you need Goron Bracelet to push in the Fire Temple. However, this one instead of ground jumping you can Clip through it to save even more time. Note: There is also a block you need to push in the room before this room, however that block is pushable without and strength upgrade.
Use the Spirit Temple Silver Block Skip to bypass the need for the Silver Gauntlets here.
You can skip the trials completely with a few techniques. You can also abuse a glitch with the center room of Ganon's Tower. As it turns out, the light beams in the center room of Ganon's Tower are never unloaded when you leave the main room. If you keep re-entering the main room, more and more copies of the light beams will be created, until a point is reached where there isn't enough memory to load the large block in front of the Light Trial door.
The glitch will also prevent objects in the Light Trial room to not load properly. This can be fixed by reloading the room by falling OoBs somehow, or by setting a Farore's Wind point in the room. However, Ganon's Tower is not a proper dungeon, so you'll have to put it on B to cast it.