Hiding specific window (Enhanced Command+H)
Solution 1:
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...