I'm going to answer this by just giving you some ideas I have, some of them might not be true, but they might be interesting to think about. I hope that's OK.
If we did not have a Moon there would be no lunar tides. (We would still have tides caused by the sun, but these would only be about 1/3 as great as the current tides.) There would also be no total solar eclipses which I think would be a shame. We might get hit more often by asteroids, as the Moon probably takes some that would otherwise hit us, so that might have meant that life couldn't have developed so well (that's a bit speculative). There would be a lot less mythology and folk tales as the Moon has played an important part in alot of cultures (although I guess we probably would have found something else to write stories about). There would have been no "Moon Race" in the 1960s so no Neil Armstrong walking on the Moon, which is pretty important in modern day culture. It might have taken longer for Astronomy to develop as the Moon is a pretty easy target to wonder about and work out things like gravity etc. I guess there is no real way of telling how things might have turned out with no Moon so this is all a bit speculative. If you can think of any other consequences I would be pleased to know about them.
In response to your question about not having a Moon, won't the Earth spin faster if there was no moon?
Lynn: Yes, this is true, thanks for bringing it up! The Earth's rotation is being slowed through tidal interactions with the Moon. If the Moon had never existed the Earth would be spinning much faster. In fact, our day would probably only be about 6 hours long! The fast rotation rate would lead to faster winds and stronger storms. The fast rotation speed would also have implications for plant photosynthesis, and animal hunting and sleeping cycles.
If you're really interested in this subject you might want to look up the book What if the Moon Didn't Exist? at your local library. It has a whole chapter on this subject, as well as chapters on other events that could have altered the evolution of Earth.
This page was last updated on July 18, 2015.