The quasi-science of determining what kinds of life can exist that did not come from Earth - the study of possible aliens. The problems of xenobiology are all very basic - since there are no actual alien life forms available for study, the field relies on speculation, but a good xenobiologist tries to back up the possibility of his or her suggestions. Within Xenobiology, there are several interesting fields:
First, one could consider what kinds of molecules an alien life form would be likely to be composed of. Isaac Asimov did a wonderful job of this in his article, "Not as We Know It". This is largely concrete, since we do have access to all the elements, and a pretty good handle on which are common enough in the universe to become a basis for life.
Second, and perhaps more entertainingly, one can consider anatomy. This is almost entirely speculative. However, one can observe incidences of convergent evolution on Earth. These suggest that there is something that life is likely to evolve in an analogous environment, if it has similar adaptive capabilities (if the mutations aliens are likely to undergo are of a different nature, then this does not apply so well).
Third, one attempts to figure out environments that are not analogous to anything on Earth, and what life forms would live in those. Larry Niven is the best at this I can think of: he devised an ecosystem of creatures living in a gas cloud in medium orbit around a neutron star for the pair of books, The Integral Trees and The Smoke Ring. He has also devised space-faring booster trees among others in a wide variety (including creatures which evolved to live in cities and in spaceships, among the moties).
Fourth, one can attempt to think about xenopsychology and xenosociology. This is what most science fiction writers need the most. It is also extremely difficult! Many earnest attempts by Sci-fi writers to come up with genuinely alternative psychologies are pretty poor, producing a creature which is maladapted in any environment. Nonetheless, it is possible to justify some alternatives. Heinlein's Stranger in a Strange Land had a reasonably valid alien psychology... Once again, Niven scores with the moties... Other nominations would be appreciated.
Xenobiology can be taken seriously or not... Everything from the silly A Guide to Extraterrestrials, to the paranoid UFO hunters with their Grays, to the well grounded in physical chemistry work by Asimov, can be considered in the field. Even calling sections of it a science is debatable. After all, almost any claim it makes is difficult or impossible to falsify, a la Karl Popper. However, it can occasionally make predictions, such as James Lovelock's prediction of finding no life on Mars.
Lovelock predicted that Mars would not have life since its atmosphere was in chemical equilibrium. There were no unstable molecules in quantities that the presence of life would be necessary to explain. By comparison, Earth's atmosphere contains a lot of molecular oxygen. If plants weren't here to produce it, the planet would eventually rust, and the oxygen would form oxides. There are other relatively unstable gases in our atmosphere - none of these are significant on Mars or any of the other planets. There is a little more to the argument (why life would almost certainly have to disturb the chemical equilibrium), but it slips my mind. One can read more on this in his book Gaia - A New Look at Life on Earth, or, oddly enough, the appendix to the manual for SimEarth.