Some very useful keystrokes you might not know about.
This is the feature of the Mac interface I hate the most: secret key combinations that invoke useful functions.
Here is an Apple support document listing secret key strokes: OS X:keyboard shortcuts.
To put the display to sleep: press the power button for a second, or in Sierra and later, ⌘ ⌃ power (because newer Macs do not have the eject button). Before Mavericks, use ⌘ ⌥ ⏏.
To kill a hung application: ⌘ ⌥ ESC.
How to force a shutdown if the computer won't shut down normally: hold power key 10 seconds.
When booting the computer:
Choosewhile holding Option to avoid being asked if you REALLY want to restart.
After restart, an app may be unable to re-open its previous windows, and be unable to launch. Hold Shift while launching the app; this clears out its "saved state". (Thanks, MacInTouch and Matt Neuburg.)
Control-click brings up a context menu: this is the same as right-click on a two-button mouse.
Quick look: in finder, select a file or group of files and hit the space bar, and you'll get a popup window with a preview. Works for Mail.app attachments also.
Hit ⌘-space for a Spotlight search.
Screen shot. ⌘ shift 4 gets cross hairs, hold mouse, Drag, release. Picture is stored on Desktop.
Hit F9 to see thumbnails of all windows, F11 to hide all applications and see the desktop.
Right-click on the dividing line in the dock: this brings up a menu that lets you change Dock preferences such as hiding and magnification.
Control-click (or right click) on a word in some apps and choose "look up in Dictionary."
⌘-shift-M toggles the mini-player in iTunes 12