Xcode 4 - detach the console/log window
Solution 1:
Go to Xcode preferences, and open the Behavior tab.
Tell Xcode to open a tab called "Debugger" when "Run Pauses" or "Run Starts". Then run it, and break that Debugging tab out into another window (drag it off the tab bar into its own window by just letting it drop outside the current window). Now reform it to your hearts content; it will stay that way. Also don't forget the little controls at the top right of the console window that slide the local variable display out of the way so you can have a full-width console on demand. I am not sure about keyboard shortcuts for that yet.
I usually keep the Debugging tab and one other tab in a separate window, for debugging tasks, and all my other editing tabs in a different window (and the debugging window on a separate monitor with the simulator). With the settings above it also means that, while editing a debugger reaching a breakpoint, it will not interrupt my editing by suddenly bringing forth the console.
Solution 2:
Sure, create a new tab, drag it off the original window, and expand the debugger area to be the whole tab. Now, whether Xcode will remember that tab and its placement is another matter. File a bug with Apple to let them know your displeasure.
Solution 3:
Taking jshier's advice a step further, you can do File -> New Window, and expand the debug window to take up the entire window. But you have to manually expand it every time you open it. Ugh.