Credit goes to the user high and i quote.
If you are interested in climbing mountains and don't want to get banned? I Will teach you.
Basic Introduction
There is a bug in the physics engine of WoW that will let you walk and run along mountains at any angle from 60-90 Degrees.
OMFG How Do I Do This???
To do this wonderful bug you have to get as high as you can on a angle lower than 60 Degrees. After that you toggle walk by default this key is set to "/". After you are all set up start walking straight along the the mountain never walk to far up or to far down otherwise you will fall.
Hints
It is also easier to mountain climb if you go in 1st person mode so you can see the mountain better.
Learn on easier mountains first like the ones outside Orgrimmar near the zeppelin tower.
Tricks
Getting bored of the slow walking around the hills? here is a trick that can cut down the time. First get on your mount(epic is preferred). Toggle walk and line up to walk along the mountain like normal. Walk for about 2 seconds then toggle run and you will keep mountain climbing but at 5 times the speed.
Links
Large movie of it in action
http://www.warcraftmovies.com/movieview.php?id=3454
Smaller movie for bad bandwith
http://www.warcraftmovies.com/movieview.php?id=2624