How do I move my current active window from one monitor to another using a keyboard shortcut?
WinSplit Revolution can do this.
In Windows 7 you can instantly move the active window from one monitor screen to another with WIN+Shift+Right/Left.
You can try Multimon Taskbar. They have a free version. You can use Ctrl-Alt-left/right to move the window between the monitors.
You might take a look at Ultramon. It provides that feature and many more.
From the linked page:
UltraMon is a utility for multi-monitor systems, designed to increase productivity and unlock the full potential of multiple monitors.
- efficiently move windows and maximize windows across the desktop
- manage more applications with the Smart Taskbar
- control application positioning with UltraMon Shortcuts
- multi-monitor support for desktop wallpapers and screen savers
- mirror your main monitor to secondary monitors for a presentation
MurGeeMon is paid software that can move windows with keyboard shortcuts.