Here's my top-20 list of must-know shortcuts; you'll never have to move your hands from the keyboard. I've included many keyboard shortcuts you might already be familiar with; skip down the list to see the ones you don't know.
Switch between open windows Alt + Tab
Minimize/restore all but active window Windows key + Home
Minimize all windows Windows key + M
Maximize window Windows key + up-arrow
Minimize/restore window Windows key + down-arrow
Make all windows transparent so you can see the desktop Windows key + spacebar
Dock window to left or right half of screen Windows key + left- or right-arrow
Zoom in/out
(In the default view, you must zoom in before zooming out.) Windows key + plus/minus sign
Lock screen Windows key + L
Open Run dialog Windows key + R
Open Search box Windows key + F
Open Windows Explorer to computer Windows key + E
Expand Folders view in Win Explorer to show where you are Control + Shift + E
Go up a level in Windows Explorer Alt + up-arrow
Choose display mode/switch monitors
(Especially useful for presenters or dual-monitor users) Windows key + P
Launch apps pinned to the Taskbar
(1 is the left-most app; Windows Key+T cycles through all apps.) Windows key + (number 1-9)
Cycle through Gadgets Windows key + G
Rotate a picture clockwise Control + period
Rotate a picture counterclockwise) Control + comma