Here is a handy listing of the most important startup and shutdown key combinations and related techniques. Instead of giving these by the keys used, I have ordered them by function, as that is how you will want to look them up.

To enter ‘modes’:
Safe mode (no third-party startups, flush caches) – Shift.
Local Recovery mode (Recovery partition, Disk Utility, System install) – Command-R may not work in Sierra with wireless keyboard.
Remote (latest) Recovery mode (online Recovery) – Command-Option-R may not work in Sierra with wireless keyboard.
Remote (original) Recovery mode (online Recovery, 10.12.4 and later only) – Command-Option-Shift-R may not work in Sierra with wireless keyboard.
These Recovery modes differ in their reinstall options.
Hardware Test/Diagnostics mode (run hardware diagnostics) – D will not normally work with wireless keyboard or mouse.
Remote Hardware Test/Diagnostics (online) – Option-D will not normally work with wireless keyboard or mouse.
Single-user mode (command line only) – Command-S.
Verbose mode – Command-V.
Target disk mode (connected to ‘master’ Mac) – T.
Note that some combined modes are recognised: for example, Command-R-S will enter Single-user mode in Recovery, and is a neat way of altering settings such as SIP which can only be changed in Terminal in Recovery mode.

To select startup:
Startup Manager, so you can choose startup volume – Option.
Boot from CD/DVD/USB stick – C.
Use OS X startup volume – X.
NetBoot – N.
Default image on NetBoot – Option-N.
Eject removable media (optical disk) – Eject key, F12, mouse button, trackpad button.

To reset stored settings:
Reset NVRAM (PRAM) – Command-Option-P-R until startup chime.
Reset SMC – varies according to model:

• iMac and desktops – shut down. Disconnect all peripheral cables. Disconnect mains power cable. Wait 15 seconds. Plug mains power cable back in. Wait a further 5 seconds before pressing Power button to start up.
• MacBook including Air and Pro with non-removable batteries – shut down. Connect and power mains adaptor. On built-in keyboard, press (left side) Shift-Control-Option and the power button, then release.
• Older portables with removable batteries – shut down. Remove power adaptor and battery. Press and hold Power button for 5 seconds. Reconnect battery and mains adaptor.

You should normally reset NVRAM after resetting the SMC.

To run sysdiagnose, which produces a large dump of diagnostic information for Apple (or third-party) analysis – Command-Option-Control-Shift-. (period).

To shut down, restart, or log out:
To force shut-down – press and hold Power button for 5 seconds, or until shuts down.
To close all apps and then force shutdown – Control-Option-Command-Power button, or Control-Option-Command-Eject.
To force restart – Control-Command-Power button.
To close all open apps and then force restart – Control-Command-Eject.
To log out normally – Shift-Command-Q.
To log out immediately – Option-Shift-Command-Q.

Note: except in dire emergency, never turns the mains supply off, or disconnect the mains power cable, unless the (desktop) Mac is already shut down.

(Updated 21 August 2018 with combined modes.)