We show that the classes of 3-manifolds admitting (a) codimension-one foliations without Reeb components, (b) taut foliations, (c) foliations with no compact leaves, or (d) Anosov flows, are all distinct. Each of these conditions is therefore {\it strictly} stronger than the ones that precede it, in the strongest possible sense. The distinguishing examples arise from studying the structure of essential laminations and foliations of graph manifolds, i.e., manifolds obtained by gluing Seifert-fibered spaces together along their boundary tori.