Could there be life on other planets? It turns out this is not an easy question to answer at all because, for starters, scientist still argue over the definition of the term 'life'.
Since a complete discussion on which is the best way to define it would be way off-topic, we will use this widely accepted definition instead: "a condition that distinguishes organisms from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to environment through changes originating internally". We will also informally define 'intelligent life' as the condition in which a particular form of life has also developed a technology level comparable to ours.
Putting all the science fiction aside, the possibility of another form of life originating somewhere in the Universe is certainly intriguing, although it has been considered only briefly by astronomers and scientists in general due to the lack of proofs which could be found to credit or discredit this theory. Unlike Newton's Laws or Einstein's theories, in fact, the hypothesis of extraterrestrial life somewhere in the Universe is certainly not easily verifiable, not to mention the constraints dictated by the laws of Phisics as we know them, according to which, even in the event we somehow spotted an extraterrestrial civilization a million light years from here, it likely won't be there anymore by the time we try to reach them.
The most notable result in the calculation of the possibility of us contacting or being contacted by an alien civilization is a simple formula elaborated during the 1960s by Dr. Frank Drake, which uses the probability concept of independent events to calculate the number of civilizations in our galaxy that we are likely to make contact with. The formula is the following:
N = R * Fp * Ne * Fl * Fi * Fc * L, where:
N is the number of civilizations in our galaxy with which we might hope to be able to communicate
R is the average rate of star formation in our galaxy
Fp is the fraction of those stars that have planets
Ne is the average number of planets that can potentially support life per star that has planets
Fl is the fraction of the above that actually go on to develop life at some point
Fi is the fraction of the above that actually go on to develop intelligent life
Fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L is the length of time such civilizations release detectable signals into space.
Of course, this formula is vague and doesn't provide a definitive result, but is still useful in that it provides scientists with a foundation to build their estimations with - the hard part is, of course, estimating the 8 factors in the formula in order to obtain an acceptable result and, as you can easily imagine, the tuning of just a couple parameters can transform a pessimistic estimation into a very optimistic one.
In the last 50 years, scientists have tried to estimate these factors with varied results. Here are the most widely accepted ranges for each parameter:
R = 6 to 10 new stars formed per year
Fp = 20% to 60% of stars have planets
Ne = 0.005 to 2 planets per star can host life
Fl = in 10% to 100% of those planets life was developed
Fi = 0.00001% to 10% of which host intelligent life
Fc = ~1% of which forms of life are willing and able to communicate to us
L = who will keep communicating for about 10,000 years.
Drake's original estimation was N = 10, while today's astronomers believe, based on more accurate parameter estimations, that N is actually closer to 2.
Finally, you should remember that this estimation only includes civilizations in the Milky Way, and not into the entire Universe, so the number of reachable civilizations should actually be higher - although, putting time-space travel and advanced technology we can't even think of aside, one would say that greater distance tends to imply greater communication difficulties, so it's plausible to think contact with civilizations in our galaxy is much more likely than contact with civilizations outside it.