Whether to spread

Tetrahymena - ciliate protozoon
Introduction
To start with, a few assumptions:
I accept that others will not accept all of the above, for a variety of reasons. Let us say that they are positions for the sake of argument (I have no wish to offend). Anyway, starting with these assumptions, it may be argued that it would be worthwhile to spread examples of Earth derived life to other parts of the universe, whether people accompanied it or not. The active intentional spreading of life to other parts of the Universe is generally referred to as directed panspermia. In what follows, by simple life I mean predominantly small, single celled and mainly prokaryotic; by complex life I mean predominantly larger, multicelled and eukaryotic.
The dilemma
Assuming we could eventually find technical means of doing so, the major problem with spreading Earth life is that we might, by doing so, damage or destroy life that is already there (wherever there might be). We definitely don't know enough at the moment to indulge in directed panspermia without risking such destruction. To avoid such acts of potential biological warfare, we'd need to get a much better idea of the likelihood of life existing elsewhere and possibly of the specific presence or absence of life in each location (e.g. by sending probes, greatly improved telescopes to check for characteristic life spectral signatures [such as indications of methane and oxygen co-existing in an atmosphere] etc.).
The morally easier option
Life (probably simple) onto non-life
If we could identify potential targets for introducing life to, that had none there already, we could send life forms from Earth. The presence of liquid water for at least some of the time would probably be a minimum.
It might be argued that a location that could support life would already have evolved its own. This may, however, not necessarily be the case. There are places on Earth, and probably on Mars, where some life forms either do, or could probably, sustain themselves now, but in which life would appear to be unlikely to evolve (e.g. Antarctic dry valleys). Also, conditions for sustaining life may not have been present for long enough on the potential target to allow life to appear, or the evolution of life may be a less probable event that many of us would like to believe. We don't yet know enough to decide on such questions. We have not yet, for example, been able to recreate conditions where we have been able to see life arise spontaneously, so we don't know for sure what is necessary.
There are likely to be some who would argue that we should not introduce life to places where it has not already evolved because to do so would be an 'unnatural' interference with pristine other worlds. One could respond that man is a product of nature and is merely acting as a 'natural' distributive agent for Earth life, as do insects for pollen or birds for fruit seeds - just on a larger scale. It is probably pointless sophistry.
Personally, I think we definitely should try to introduce life where none already exists, but it would probably prove more difficult than if life were there already, and initially only relatively small and simple life forms could be introduced (see below). Technical means of directed panspermia with simple life forms have been proposed for many years (e.g. Meot-ner & Matloff (1979), Directed panspermia: A technical and ethical evaluation of seeding nearby solar systems, Journal of the British Interplanetary Society, 32, pp 419-423).
And the more difficult ones
Life onto simple life
Perhaps a more interesting discussion than that above would be whether we should introduce simple or complex Earth life to planets that already have simple life of their own. It has been estimated that for the first 2 or 3 billion years, life on Earth was single celled, probably with variants of archaebacteria, eubacteria and unicellular protoeukaryotes. The emergence of multicellular life forms may have only taken place as recently as the last 0.9 to 0.6 billion years. It is still a matter of dispute as to whether this was by chance or an inevitable result of the changes in the environment brought about by the activities of the simple life forms (e.g. an oxygen atmosphere) or by physical changes in the Earth/Sun system. It is obvious that simple life has, at least, the potential to evolve to give more complex forms (whether this is inevitable or not). So, the question again, should we introduce simple or complex Earth life to a planet that already has simple life? What would it do? What damage could it cause (or what good)?
Complex life onto simple life
Consider first the situation with complex life. One thing that could be said is that it would probably be very difficult to introduce complex life unless simple life already existed, since (almost) all complex life requires an oxygen atmosphere and that probably does not arise on a planet as a result of physical processes, but only through the activities of simple photosynthetic organisms like blue-green algae (more properly, blue-green bacteria) (there are a few eukaryotes that don't require an oxygen atmosphere, but they usually require other life products such as fermentable complex molecules to survive and some of them even require the gut of a larger animal to live in). OK, so you could introduce complex life if simple life already existed, but that doesn't say that you should. What would be the possible effects of such an interference? On Earth, the evolution of complex multi-cellular life forms did not lead to the extinction of simpler forms. Unicellular organisms are still present in huge numbers and variety and are the dominant component of many geochemical cycles. The evolution of an oxygen atmosphere itself probably had more effect, in terms of extinction of other simple life forms or their restriction to certain sites, than did any more complex life that followed.
That said, the introduction of complex life forms to another planet could be, in many ways, different from the situation when complex life forms evolved on Earth. For example, all life on Earth uses almost the same genetic code, although there are minor variations (e.g. in Tetrahymena, a ciliated protozoan, the UAA codon codes for the amino acid glutamine, whereas more generally it codes for a stop; similarly, in human mitochondria, the AUA codon codes for methionine whereas in the nucleus of the same cell the same codon would code for isoleucine). It is not known whether the code is the way it is by chance or was directed into its current form by some unknown predisposition for a particular genetic arrangement to give a particular amino acid. Thus it is unknown whether, even if life on another planet was carbon based and used arrangements of three bases to encode amino acids, it would use the same arrangements of bases to give the same amino acids. The chances probably are that it wouldn't. Would new life forms with a completely different genetic code be able to co-exist with the original life forms? The example of the human mitochondrion and nucleus suggests that this must be possible (although the differences are not great in that case) and that life forms with different genetic codes could co-exist. Such a situation would have the interesting side effect that the viruses of the original would be unable to successfully replicate in the introduced life, and vice versa, since the viruses' nucleic acids would be incorrectly translated and transcribed in the new host. Incidentally, the presence of an (almost) universal genetic code on Earth may also be taken as a pointer that life here arose in-situ on one occasion, or that if it arose by directed panspermia it probably only happened (successfully) once (again unless, as discussed above, the code is not as arbitrary as it appears).

Mammalian mitochondrion
An alternative possible difference arises from the fact that amino acids can exist as two different optical isomers, such that a solution of them can rotate the plane of polarised light either to the left or the right. All life on Earth uses amino acids that are laevo (left) rotatory. As with the genetic code, we don't know whether this is a result of random chance in the original life forms on Earth or whether it has a more definite determinant. If it is the former, then life forms on other planets could arise using dextro (right) rotatory amino acids. Again we don't know whether Dextro and Laevo rotatory life forms could co-exist. There are no known examples of this on Earth. It may, for example, be difficult for a laevo rotatory predator to exist by eating dextro rotatory prey, as the proteins of the prey may be of little nutritional benefit to the predator. Thus sharing of food webs would be unlikely under such circumstances.
Even more extreme differences are possible such as the use of different, as yet unknown, information molecules than nucleic acids or different major structural molecules than amino-acids/proteins. Yet more extreme still would be life based on a different major structural element (e.g. the oft discussed silicon rather than carbon).
If we were to introduce complex life forms that could survive by eating the simpler life forms that were native to the planet, the chances are that they would do so. This would not necessarily be an entirely bad thing. 'Cropping theory' suggests that the evolutionary explosion of the Cambrian period on Earth may have been assisted (i.e. speeded up) by the pressure from predators. Thus the introduction of life forms from Earth could act as an evolutionary trigger for the native forms, reducing their 'lag' period of apparent evolutionary stasis such as appears to have happened on Earth. Then again, it is only a theory.
Simple life onto simple life
It seems inevitable that an introduction of complex Earth life would result in some effects on any simple native life that existed, be those effects good or bad (a judgement which would inevitably be affected by the point of view of the judge). However, it is also important to bear in mind that it would be impossible to introduce complex life forms without also introducing the simple life forms (e.g. bacteria) that are always their companions. Thus, as well as potentially suffering predation, for example, from Earth life that was larger and more complex than it, simple native life forms would also be exposed to competition for resources and in some cases predation and parasitism from smaller, simpler, Earth life, which would almost certainly be a more potent interfering factor. To illustrate the impossibility of avoiding the introduction of simpler Earth life, consider the most complex Earth life form, us. At any one time our gut contains a greater number of non-human cells (mainly bacteria, plus a few yeasts, protozoa etc.) than there are human cells in our entire body. Even assuming that you could sterilise the gut and still remain healthy (difficult), the human skin carries a vast and diverse microbial flora that can be very difficult to eradicate, as has been discovered for hospital workers unfortunate enough to be chronic shedders of Staphylococcus aureus who have had to give up theatre duties to avoid patient wound contamination. Even less fortunate are those individuals cursed by carriage of anaerobic bacteria such as Clostridium spp. in their hair follicles and sweat and sebaceous glands. Some of these bacteria can produce very strong odours that make life very difficult for the human host, and they have, in some cases, been found to be resistant to all attempts at removal including antibiotics, hyperbaric oxygen, severe washing and surface application of strong disinfectants. Similar arguments, different in their specifics, would probably apply to any complex Earth life form that we could consider introducing.
The science fiction scenario of people landing on a planet bearing alien life would thus carry with it consequences beyond those traditionally considered of just whether we would catch a disease or be eaten by the native predators. The microbes of our wastes and dandruff could be starting to compete with native flora and fauna from shortly after we arrive, and the same would apply to any Earth life forms introduced to a new, life bearing, planet. Even if the native life were radically different and based on a completely different biochemistry it is unlikely that Earth life could be successfully introduced without having an effect, since it is known that life on Earth affects non-biological chemistry as well as that more obviously and intimately involved with life (e.g. weathering of rocks, laying down of rocks, aquatic pH, atmospheric composition). It would be like Europeans introducing smallpox to the Americas, but on a much much larger scale. Could we do this? Probably yes. Should we do this? Probably no.
Life onto complex life
Even more tragic would be the damaging or destructive introduction of Earth derived life to an ecosystem that had already evolved more complex life forms, particularly sentient ones. It may be true that we could readily detect a technological civilization by, for example, radio emissions. However, we've only been emitting such for about a hundred years, whereas we have been sentient, probably, for millions of years, and there still exist on this planet sentient species with a technology that would be undetectable (e.g chimpanzees). This argues even more strongly for care about scouting potential directed panspermia sites before we try the process.
Would we be good?
Be the life complex or simple, sentient or otherwise, if we find it, would we be prepared to deny ourselves the possibility of colonising what would probably be the best places elsewhere in the universe? Our current behaviour as a species shows that we'd rather eliminate a species of fish than make a minor alteration to our diet, even though the act of destruction leads to the change of diet anyway. Further, if we look at our treatment of the chimpanzees, it would suggest that we'd casually wipe out another sentient life form if it was in any way convenient to us to do so. I would argue strongly that we shouldn't, but most people wouldn't listen. Thus, it seems likely that we would also be prepared to risk the destruction or drastic alteration of life on other planets if to do so suited our whim. If the Earth itself were threatened with destruction the qualms over interplanetary morality would almost certainly be dismissed. Perhaps the consolation in all of this is that life may be rare, complex life probably even rarer and sentient life still more so, so perhaps we'll only ever get to test our interspecific morality on the species with which we currently co-habit.

Anabaena - blue-green alga