The moon was a lot closer to the earth billions of years ago, and the tides were much bigger then. One theory I've come across in the past is that this created the enviromments in which life first started. There are other theories of course, such as that it formed about the black smoker vents under the oceans, but the tides will have been an important route for life to follow from the sea to dry land. One thing is certain and that is thst the moon stabilises the earth's rotational spin - without a large moon, the earth would wobble much more than it does, and sometimes it's axis would be much closer to it's plane of orbit around the sun than it ever gets now. That would be very bad news because there would be intolerable summers and winters that complex life couldn't survive. This is one of the reasons I think we might be the only intelligent life in the Galaxy - because it will be a pure very low-probability fluke that a planet like earth has such a moon to keep its environment so stable for billions of years.
Does the moon have other effects on us - I don't know. One of my difficulties with astrological influences on people is when you think of the not impossible idea of relocating to, say, Europa. Would that break the influences - it would certainly impact on the relationship between myself, the planets, the sun and the fixed stars, so there would have to be a generalisation of the astrological model that allows translation according to where in the sloar system you were located. Would Io, Callisto and Ganymede replace the moon as the points of influence? And then what happens if you go further ahead in time to when we can travel to other solar systems? How would the astrological concept cope with such a relocation, and would there have to be a new one constructed around the planetary components of that system and where you were located within it? But I do think that the moon affects our moods sometimes - there is something enchanted and soul-expanding about a full moon rising over the snow on a cold snowy landscape.