Off = all components turned off. No battery drain (though batteries lose a little bit of charge each day just sitting on the shelf).
Hibernate = contents of memory written to disk, all components turned off. I recommend disabling this if you have a SSD, as often it takes longer to wake from hibernate than to just boot up on a SSD. I've also found it a bit flaky in Win 8.x, so usually just disable it anyway.
Sleep/Suspend = CPU and memory kept powered on (in a low power state), everything else turned off. Your battery will slowly drain in this state.
There's very little difference in terms of component wear. The main reason to use Sleep is if your computer takes a long time to boot, or if you like to pick off right where you left off with your browser, apps, and windows already open and in just the right place. The main reason to turn it off is if you absolutely must have every drop of battery life when you turn the laptop on.
For a desktop, i usually recommend turning it off at night. A power failure when the desktop is in Sleep acts like a crash - the computer will have to scan for and recover damaged files. In very rare cases this can cause the computer to fail to boot, which is a major headache I'd rather not visit my friend's house to fix. A power failure when the desktop is off has no consequences.