I was watching a video lecture from iTunes U., where instructor showed how one can take a debugger section of the Xcode and was able to pull that window away from the main.<
Open a new tab, show the debugger (cmd-shift-Y) and drag the divider all the way to the top. Close the navigator (cmd-0) and inspector windows (cmd-opt-0), then drag the tab off into a new window.
If you name the tab before you tear it off, e.g., "Debugger", then set up a Behavior in Xcode's preferences ( Preferences -> Behaviors -> Run Starts -> Show Tab "Debugger" ), it'll show that window when you run your app. It'll even recreate it if you close it.
If you have access to the WWDC 2011 videos, "Maximizing Productivity in Xcode 4" has a lot of great info.
Here's a screenshot before tearing the tab off:
I know it's a little too late, but I'm going to be borrowing from this answer. Go to your preferences, go to the behaviour tab. Change the running behaviour to show a new window.
If you don't want the window to have an editor or toolbar, you can customise it that way too.
Xcode 11
Change behaviour
Xcode -> Preferences... -> Behaviors -> Running -> Starts -> Show tab named <tab_name> in active window
After that <tab_name> tab will be opened automatically
To create a new tab manually:
File -> New -> Tab
Window -> Rename Tab... -> <tab_name>