How do I remove the Unity launcher?
In 12.04, you can go to System Settings > Appearance > Behavior and turn on autohide, then turn the sensitivity all the way down. Now the launcher will only show when you press Super.
Install ccsm (Compiz Config Settings Manager)
Launch ccsm and click on the "Unity Plugin"
Under "Behavior", change "Hide Launcher" to "autohide"
Change "Reveal Mode" to None.
Disable "Key to show launcher" and "Key to put focus on launcher"
*Disabling "Key to show launcher" may prevent you from accessing the dash. If you omit this part of step 5, you can access the dash, but the launcher will appear non-invasively while the dash is displayed. I don't know of any way to stop this.
Update: 12.04 does things differently, thus this may not work after 11.10.
In simple words: you can't. By design, the launcher is intended to stay there always. If you want to give it up, the only way to do so is to give up the entire unity interface by switching to some other DE or by switching to the classic GNOME session.
Moving the launcher to some other edge of the screen is also not implemented and wouldn't be, as per Mark's comment on a bug.