Well it would be a lot darker at night without the Moon, and what would werewolves howl at?
The tides are ‘controlled’ by the Moon so we’d have about 1/6th of the tides we have today (there is some control on tides from the Sun). Pretty much there would be a smaller difference between high and low tide.
There is also something called tidal friction which slows down the Earth’s rotation so instead of being 24 hour days we would have around six hour days.
The Earth also wobbles a bit on it’s rotation which is counter acted by the Moon. Without this the North Pole wouldn’t be North but could be at the equator instead which would make our temperature pretty crazy!
This might also affect how we evolved being in different climates but I’m not wholly sure on that one.