There are several scientific lines of thought on extra-terrestrial life. Several of the most common are mentioned in this summer's movie Contact, based on a book by E.T. life guru Carl Sagan. One such chain of reasoning, not quite explicitly mentioned but hinted at, in the movie is the so-called Drake Equation (The SETI Institute), named after Frank Drake, who arranged the meeting at which the equation was first formulated. The number of intelligent civilizations at a given time is given by,
N(intelligent civilizations)
=
R*(number of suitable stars created per year)
fp(fraction with planets)
fe(fraction of earth-type planets)
fl(fraction with life)
fi(fraction which is intelligent)
ft(fraction which is technological)
L(lifetime of technological civilization)
This number was estimated by Sagan to range between 0.1 and 100 within the galaxy, with the largest uncertainty given by the lifetime of a civilization.
Since his estimate a few of the factors have changed. The lifetime has probably increased since the Cold War ended without a nuclear war. The fraction of stars with planets has certainly increased (see my Jan 1998 edit), and the fraction of those with life has probably increased (ibid). However, one rather daunting factor is that the radio signals we are emitting are decreasing rather than increasing, due to increased use of satellite and cable communications so that in the future, it's not clear if Earth will be detectable as intelligent from any distance (as supposed in Contact), so there is little reason to guess that a civilization would be detectable in the radio spectrum, unless it specifically tried to be.
While the Drake Equation is the most elaborate and most recognizable argument regarding E.T. life, there are certainly many others. Freeman Dyson has suggested that ultra-intelligent civilizations would have built massive spheres around their stars to harness all the energy possible. These spheres would emit waste heat in the infrared, and would be very obvious in infrared studies of the sky; none have been seen. Enrico Fermi has pointed out that a robust civilization would be able to colonize all compatible planets in the galaxy within a million years or so. Given that stars are billions of years old, we would have to expect that such civilization would have long since colonized the galaxy and certainly earth. So where are they?
Another argument is a recurrent point in Contact: that if we are the only life in the Universe, it seems like "an awful waste of space" — this point is perhaps the most valid and most potent. Here, we are invoking the "Copernican Principle" that states that we, as observers, are neither particularly special, nor particularly lucky. This issue is confused by the fact that whether we were lucky or not, we are here nonetheless. However, some rational points can be made:
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