Invisibility (Horde)

First of all you need a charakter of the horde. Next it should be a mage, but maybe this works with the hearthstone, too. I haven't tried this yet. Now, go to silverpine forest. You have to accept the following quest: Welcome to the Machine (Quest:Welcome to the Machine - WoWWiki - Your guide to the World of Warcraft) 
Now.. Stand near the horse which you can mount on. Use your teleport to undercity.. And now klick on the horse as fast as you can - You have to click while you port yourself. If you got the right timing, than congratulations - Noboy can see you anymore for the moment.
Yes, you stand at the mage quarter of undercity and you can do whatever you want - You can cast, you can mount.. Feel free yourself to explore it.

Some facts:

• You cannot see any NPCs, players and game objects anymore. (If you want to leave undercity, use the canals.)
• You can leave the zone and you will be invisible
• Invisibility holds on until you relog or get a loading screen
• You can use all channels and you'll be showed in the /who correctly, even if you leave UC.. Or you can go in a group with someone - He can see your point on the map!)
• If you relog, you'll stand where you logged out. (Because you're not in Otherworld.)

Now you can go through the world, you can maybe run through stormwind or ironforge, relog and now you've passed through much enemys. Or you can do exploring achievements without any danger.
Maybe you can fish, but I haven't tried this.