Bookmarklet

1. Right-click the following link: Random YouTube Region, and choose Bookmark This Link… / Add Link to Bookmarks… / Add to Favorites… as appropriate for your browser.
2. And that’s it.

If you want to make any modifications, here’s the original code:
javascript:(function(){switch(Math.floor(11*Math.random())){case 0:location.href='http://br.youtube.com/';break;case 1:location.href='http://de.youtube.com/';break;case 2:location.href='http://es.youtube.com/';break;case 3:location.href='http://fr.youtube.com/';break;case 4:location.href='http://ie.youtube.com/';break;case 5:location.href='http://it.youtube.com/';break;case 6:location.href='http://jp.youtube.com/';break;case 7:location.href='http://nl.youtube.com/';break;case 8:location.href='http://pl.youtube.com/';break;case 9:location.href='http://uk.youtube.com/';break;default:location.href='http://www.youtube.com/';}})()
It has to be on a single line to fit in the location field of your bookmark.

Firefox Extension

1. Right-click the following link: RandomTube Extension, and choose Save Link As… or your language’s equivalent.
2. Once the file is saved, drag it into the Firefox window to begin installation.
3. Restart Firefox when prompted, and RandomTube is ready to go.

Known Issues (version 0.4.1)

• Not all links are rewritten. A few use scripts to determine their action which makes them much harder to alter, but most are rewritten with a random region.
• There are only three localisations at the moment – British English (en-GB), Deutsch (de), and American English (en-US). This does not affect the extension’s functionality, only its user-friendliness for most of the world’s population. Unfortunately, I’m not sufficiently proficient in any other languages to make any more translations.