Shut your 'puter down or leave it 'on'?

S1 (CPU stopped, RAM refreshed, running in low power mode)
S2 (CPU off, RAM refreshed, running in a lower power mode than S1)
S3 (traditional Standby, with the CPU off and RAM in slow refresh)
S4 (Hibernate, with the hardware off and system memory saved as a temporary file)

S0 is On and S5 off

You can see more (and detail info) here: http://msdn.microsoft.com/en-us/library/windows/hardware/ff564575(v=vs.85).aspx

WOL and WOI just work with S3 mode.