iMac's screen turns itself on

I never turn my iMac off. When I leave, I turn it's screen off.

BUT

1. iMac's screen turns itself on for whatever reason and remains on. I need to log in in order to turn it off again.
2. If I don't turn the iMac's screen off, it remains on all the time.

Note: I did an NVRAM, checked my Energy Saving Preferences and so forth. Problem has been on for months.