Tools (SSMS, Agent, Profiler, etc.)
An option that says, "New Query windows inherit properties from window in focus" or something along those lines. Settings I think are useful include the results to mode, include actual execution plan, and any other window-level settings that are *not* default for the window currently in focus. If no window is in focus (e.g. context is on the properties panel, object explorer, etc.) then this setting should be ignored.
Barring an option to set the default behavior, how about an option on the right-click context menu that says, "open a new query editor window with these settings"? This is probably much less work to implement but would still achieve the goal. Added bonus would be a keyboard shortcut to complement Ctrl+N, or at least the ability to set up a custom shortcut that maps to the same behavior.