Check out this article from Astrobiology Magazine, describing how things would be different if we lacked the moon. Here's a sample:
There are some very subtle effects of the Moon in the climate and the oceans. One pattern that has been found recently is related to the Pacific Ocean's El NiÃ±o phenomenon. You have a cold undersea current coming from the Antarctic sea, and that creates the Humboldt stream which keeps the sea around the South American coast near Peru and Chile quite cold. Because of this, there are fewer clouds and less precipitation there. Sometimes this current drifts away from the coast, and then you have much more cloud formation and a period of very bad weather over South America. Satellites have monitored this stream over the Pacific Ocean and they have found some streams which were not known before. They can connect some of these streams with how the Moon's tidal effect influences the mixing of the deep ocean. There was a French-American mission called TOPEX/Poseidon that accurately measured the altitude of the sea and detected a little stream a few centimeters high. That doesn't seem like a lot, but over the whole area of the Pacific Ocean it represents a huge amount of water transferred from one place to another.
If you would take away the Moon suddenly, it would change the global altitude of the ocean. Right now there is a distortion which is elongated around the equator, so if we didn't have this effect, suddenly a lot of water would be redistributed toward the polar regions.
Read the rest for a fascinating piece of speculative science.