Edit 4/25/12: New run, 22:00! http://www.youtube.com/watch?v=J3GfV-...
Edit: Since this exploded in popularity and I'm getting a lot of the same questions, here's an FAQ. Please read before commenting
Q: Why is this on the Japanese version?
A: The text is much faster. Other than that, it's the exact same as any other version.
Q: Is this legit?
A: Yes, everything I do here can be done on any regular console with no cheats or modifications at all.
Q: Why do you need the bottle?
A: To activate the ocarina items glitch on the edge of the blue warp which allowed me to move during the cutscene so I could get to the door.
Q: How does that warp glitch work?
A: The game is trying to load the value for the kokiri emerald cutscene and the main deku tree area at the same time, so it sends you to a new room value which happens to be a room in the escape.
Q: How did you die to gohma? Was it on purpose?
A: I got hit at the same time I killed her which also killed me. It was on purpose, I needed to return to the room with the stone wall blocking the door gone.
Q: What's up with the deku sticks?
A: They are actually as powerful as the master sword, so they're a great weapon for this.
Q: How did you figure this out? Was it on accident?
A: First of all, I did not find this, it was found by r0bd0g and sockfolder.
It was found by examining older glitches and trying to do it with a different method. The warp itself was possible with farore's wind on B as adult, but took too long to do that so no one really cared. Then the idea of using the door instead of farore's wind was proposed, it was tested, and it worked.
I have now beaten this run with a time of 22:42 (World Record as of 4/15/12), which you can watch here http://www.twitch.tv/zfg1/b/315135377 . I didn't bother uploading it to youtube because I'll probably beat it again soon and don't want to end up uploading 10 runs of the same category with a few seconds difference each.
This beats my last run by a little over 2 minutes, mostly just from optimization and not playing bad. The biggest improvement from this run would be killing gohma in 1 cycle, but doing that and dieing at the last hit is pretty hard. A run that can get 1 cycle gohma and generally better play should be about a minute faster.
I'll be streaming speedrun attempts for improving this over the next few days on my twitch.tv page http://www.twitch.tv/zfg1