You fire up chrome to test mobile project x, or iPad project y. Next thing you're doing is undocking web inspector so isn't constrained to the dimensions to which you've resized the browser. But then you have to cmd-` or alt-tab between the console and the page you're working on. Annoying. And if you happen to have two of these, it can be even more annoying to keep track of what undocked web inspector belongs to what page.
To dock to right, open the Web Inspector, click on the gear icon at the bottom right, and check "Dock to right". This feature was made available in the stable channel on Mar 28/v18, so you should either have it or just need to update. You may also be able to accomplish this through the UI element that would normally undock the console - instead of just clicking it, click and hold, and it turns into a little iconized menu where the menu item is a toggle for dock right / dock bottom. One long click vs. 3 clicks - even better!
This feature is fantastic for working on mobile and ipad in portrait mode, but it can also be handy for working on fixed-width sites since they're usually <1024 wide, and you've probably got 1920 pixels of width to work with.
Thanks Chrome/Webkit devs!