Jaws and branchial arches together are a basic, segmented feature of the vertebrate head. Seven arches develop in the zebrafish embryo (Danio rerio), derived largely from neural crest cells that form the cartilaginous skeleton. In this and the following paper we describe the phenotypes of 109 arch mutants, focusing here on three classes that affect the posterior pharyngeal arches, including the hyoid and five gill-bearing arches. In lockjaw, the hyoid arch is strongly reduced and subsets of branchial arches do not develop. Mutants of a large second class, designated the flathead group, lack several adjacent branchial arches and their associated cartilages. Five alleles at the flathead locus all lead to larvae that lack arches 4–6. Among 34 other flathead group members complementation tests are incomplete, but at least six unique phenotypes can be distinguished. These all delete continuous stretches of adjacent branchial arches and unpaired cartilages in the ventral midline. Many show cell death in the midbrain, from which some neural crest precursors of the arches originate. lockjaw and a few mutants in the flathead group, including pistachio, affect both jaw cartilage and pigmentation, reflecting essential functions of these genes in at least two neural crest lineages. Mutants of a third class, including boxer, dackel and pincher, affect pectoral fins and axonal trajectories in the brain, as well as the arches. Their skeletal phenotypes suggest that they disrupt cartilage morphogenesis in all arches. Our results suggest that there are sets of genes that: (1) specify neural crest cells in groups of adjacent head segments, and (2) function in common genetic pathways in a variety of tissues including the brain, pectoral fins and pigment cells as well as pharyngeal arches.