In Windows I can use the "Windows Key + Arrows" snap feature to quickly move windows between monitors in a multi-monitor setup. I'm looking for a way to do this same thing in Linux. I've tried Cinnamon, KDE, and XFCE and haven't had any luck figuring out how to get this functionality in any of those DEs.
I use KDE and there is a keybinding for this. From the K menu, run "System Settings" (you can search for that phrase in the search field if the icon is not already showing). Then go to "Shortcuts and Gestures", then "Global Keyboard Shortcuts", choose "KWin" from list of KDE components. There is an action called "Window to Next Screen". Assign a hotkey (I use Ctrl-Alt-Shift-Right) for mine. It's strange that there isn't a hotkey for Window to Previous Screen. But, since I only have 2 monitors, it acts as a toggle between the left and right monitor. I should add that I'm using Linux Mint 13 64-bit with KDE 4.8.5.