Hiding specific window (Enhanced Command+H)
This may not be exactly what you are looking for but it is a start.

If you want to hide your current front most (active) window simply pressing ⌘ Command M will do that.

That is the keyboard equivalent of clicking the yellow "Minimize" window button. 

If you then need to "un-minimize" a window that you recently minimized that will require a trip to the mouse and the right size of the dock...