Moon's Role
Although the moon on earth plays some intricate roles in regards to nature, its absence wouldn't prevent life from forming on earth. Plants stay alive based on light from the sun, as well as water, making them completely independent of the moon. The moon's central effect is causing ocean tides to move in and out -- as they are pulled by the moon's gravitational force and earth's rotation. The tides have caused many creatures to evolve with adaptations that depend on tides.
Life on Moons
Not only does a planet not necessarily need a moon for life, but life may also evolve on the moon itself. Moons throughout the solar system have different compositions, some of which are rock-based, much like earth's moon. Others -- such as Saturn's moon, Titan -- are composed of mostly nitrogen; however, Titan also contains liquid methane lakes that may harbor life. The lakes are thought to stay liquid because the immense gravity of Saturn is thought to constantly bend the planet, preventing freezing.
Necessities for Life
Necessities for life are constantly changing, usually leaning towards fewer requirements. What is known is that if ice is present on a planet, it is highly likely that small bacteria exist. This is one reason why astronomers are so interested in exploring Mars, which contains ice caps that may even harbor water in underground reservoirs.
Probabilities of Life
The probabilities of life expand with each discovery scientists and astronomers make. As technology increases, astronomers are now able to detect planets orbiting around suns, which are normally extremely hard to detect as they don't send light in the way suns do. The first planet thought to be the correct location for life to exist is Gliese 581g. This planet orbits around a red dwarf star that is around 20 light-years in distance.