When debugging mobile sites, docking to the right makes good use of the space available to you, and allows you to quickly change the space shared between the Developer Tools and the browser view area to try different widths.
In Chrome Developer Tools and Opera, the bottom left icon allows you to change the dock settings of your Developer Tools. A single click switches between docking at the bottom and the right.
In Chrome Developer Tool settings under the "General" tab, you can also change the appearance of the tools so that panels are split vertically.
In Opera also you can split the panels vertically under the "General" tab of settings.
In Firefox Aurora, you can also dock to right and take advantage of this trick.
Firebug was the first to offer this trick.