There is a quite famous formula in science called the Drake Equation. It was developed by Frank Drake, Emeritus Professor of Astronomy and Astrophysics at the University of California, Santa Cruz in 1961 as part of the SETI programme, and it sets a framework for trying to estimate the number of detectable extraterrestrial civilisations in our galaxy, the Milky Way. I'm going to bore you now with the basic details of this formula, because I find the concept of it quite interesting. So in all it's glory here it is:
That looks pretty meaningless, so let's break it down a bit:
N is the number of civilisations within our galaxy with whom we may be able to communicate, i.e. the target number we are interested in.
R* is the rate of new star formation in the galaxy.
fp is the fraction of these stars which have planets in orbit.
ne is the number of planets in each star system which may be capable of supporting life.
fℓ is the fraction of these planets which actually go on to develop life
fi is the fraction of these which evolve intelligence
fc is the fraction of intelligent civilisations which have detectable interstellar communication.
L is the length if time during which each civilisation emits detectable communication.
I won't go into the details of each of the factors, but if you want to read more follow the link above to the Wiki page. Current best estimates of the various factors leads us to a final N number of somewhere between 0 and 182,000,000. This varies mainly because the actual values of several of the factors are a matter of some conjecture, and we are forced to guess what these might be. In particular the values for fℓ fi and fc are open to debate, because we have no data on which to base our estimates. So we may be alone, or our galaxy may be teeming with intelligent life we are yet to discover. However because of the vast distances involved (the Milky Way is a spiral galaxy roughly 110,000 light years across containing around 300 billion stars) if the number of detectable civilisations is moderate (say 10,000 or so) they may be sufficiently far away that we can't find them with our current level of technology, and any signals being emitted by them may not have reached here yet, and may not do so for hundreds or thousands of years.
As stated above there is a lot of conjecture about the values of some of the factors, leading to such a wide variety of possible answers that its use as a predictive tool is questionable. It does, however, provide an interesting starting point to stimulate thought about the likelihood of extraterrestrial life. Unfortunately it is unlikely to be a successful conversation starter at the vast majority of social functions :)
One of the more interesting possibilities raised by the Drake Equation, and one for which we are now beginning to be able to assign numbers, is the likelihood of life existing elsewhere, even in its simplest form. We already know the rate of stellar formation, and therefore the number of stars in our galaxy, and we are starting to be able to make good guesses at the number of these with planets, and what proportion of these planets lie within the goldilocks zone, the orbital distance at which liquid water might exist on the planet's surface, and therefore the zone in which life as we know it is most likely to arise. Our assumption is that life is pretty likely to arise where conditions exist which favour it. This is based on studies of the diversity of life on Earth, the one place where we know with certainty that life has evolved. Life inhabits pretty much every available habitat on our little ball of rock, and manages quite nicely in environments you and I would find quite unbearable. So it doesn't seem unreasonable given favourable conditions that at some stage elsewhere a complex organic molecule began to replicate itself. If we replace R* with the total number of stars in our galaxy (300 billion) to get a current snapshot and then use conservative estimates N becomes:
300,000,000,000 x 0.34 x 0.005 x 0.13 = 66,300,000
That is over 66 million planets or moons in the Milky Way which may contain even rudimentary life as we know it. In our own solar system there are a couple of reasonable candidates. Mars is a possibility. We know water ice exists on the planet, and at some stage in the past it had liquid water on its surface. Recent photographs suggest the existence of subterranean caves, and it is likely that ice exists in a sort of permafrost under the soil surface. Both of these habitats support basic life on Earth. A more exciting possibility is Europa, a moon of Jupiter. Like Earth it has a metallic core surrounded by rock. The entire surface is covered by a layer of water roughly 100km thick. The massive gravity of Jupiter exerts strong tidal forces on this layer, which creates sufficient heat through friction to allow a significant ocean of liquid water to exist underneath the icy exterior. And anywhere where we see permanent liquid water there is a strong likelihood that life may exist. Hopefully the question will be answered one way or another when the Jupiter Icy Moon Explorer investigates Europa around 2030. I can't wait :)