As this question, or something close to it, comes up often, in various sections of BAUT, I thought it would be a good idea to have a thread devoted to it.
First, some words on scope. This thread is primarily about the sets of observations, done by astronomers and others, which have lead to the idea of dark matter being fully accepted by the astronomical community. Of necessity, some theory will also need to be covered, particularly General Relativity and Newtonian dynamics.
Two classes of 'dark matter' are somewhat tangential to this thread - 'hot dark matter' ('dark matter' which is, or was, moving at relativistic speeds; neutrinos are an example), and 'baryonic dark matter' (or 'ordinary matter' - atoms and molecules and ions of H, He, ..., whether in the form of plasma, gas, dust, or bigger clumps that does not emit detectable electromagnetic radiation; this also includes baryonic matter in the form of white dwarfs or neutron stars).
Recently, a good, popular-level book on DM has been published by Springer-Praxis "In Search of Dark Matter", Ken Freeman and Geoff McNamara (ISBN 0-387-27616-5).