Q:

Why do speed-runners usually use the Japanese version of a game?

In most speed-running videos, the person playing the game will usually play the Japanese version, with or without any knowledge of understanding Japanese. Is there a reason why they do this? 
In particular, I am talking about traditionally Japanese games being speed ran, like Cave Story or Legend of Zelda. 

A:

There's a few reasons why a given release of a game (Japanese vs International, NTSC vs PAL) is used for any given run, and they change depending on the game. That said, there's a few common reasons:

NTSC (Japanese or US) instead of PAL (European): While this is less of an issue in newer games (AFAIK), the major difference here is refresh rate (which in itself affects frame rate). NTSC uses a refresh rate of approximately 60Hz (I want to say it's 59.94Hz, but for simpler math, let's go with 60Hz), while PAL uses 50Hz. Almost everything about a game in older games is tied around this refresh rate, so input checking, frame rate, and so on is all based on the "refresh rate clock". In the majority of cases, NTSC wins out for speed due to being about 17% faster, although there are a few cases where PAL is actually faster due to certain major time-saving techniques being unfeasible at the faster 60Hz rate.
Actual code differences/revisions: Certain games are actually more buggy in some releases (usually the older ones which are typically the Japanese release, although again, this has exceptions) and these bugs can be used for faster runs.
Characters-per-second in text: For games that have character-by-character text (e.g. Legend of Zelda), the Japanese version will usually see a significant time gain just by virtue of the use of kanji and the Japanese syllabaries (hiragana and katakana).

A:

Since you asked about Legend of Zelda specifically: Cosmo, the former (non-tool-assisted) speedrun world record holder for Ocarina of Time, released a very cool annotated video explaining the glitches and history of his speedrun.

At about 3m44s:

This run was done on the official Chinese release of the game.  I chose this version because of faster text and less lag.

If you haven't seen this video before, I highly recommend it - it gives a great look into the world of speedrunning.

A:

Sometimes they use Japanese or American versions as they run in 60hz which way more faster than European/Australian (PAL versions) ones which run in 50hz.
It's 17% faster. This ratio is computed like this : 100-(50*100/60)
60hz means 60 frames per seconds, as 50hz means 50 frames per seconds. So with 60hz you have more frames to enter inputs (mostly used in tool assisted speedrun). 
Take a look at frame rate on wikipedia.

