If a human colony is set up on another planet or moon, or in an orbiting habitat, most of the infectious diseases from Earth would not be present in the small initial population. Careful screening could further reduce the number of infectious diseases introduced. Would the human immune system suffer problems if infection is reduced too much? Would we need to take some token infections (such as the cold) with us?
This is difficult to answer definitively. Certainly, humans require certain microorganisms in order to be healthy, and the effect of carrying around such microorganisms is that with their shorter generations, the probability of a mutation making the organism pathogenic is small but significant.
However, it is difficult to say if a lack of pathogenic organisms is deleterious. As an undergraduate student of human physiology, I have developed the hypothesis - as yet without any proof either supporting or disproving it - that the human/mammalian immune system has evolved to expect a certain level of exposure to pathogens which would require an immune response, and if such a level of exposure is not achieved, the likelihood of autoimmune diseases is elevated.
Hence, our habit of sterilizing everything our kids come into contact with could well have the effect of setting them up for an autoimmune disease later in life. To not have any pathogens at all? That could be disastrous, or not.