The ability to disperse over long distances can result in a high propensity for colonizing new geographic regions, including uninhabited continents, and lead to lineage diversification via allopatric speciation. However, high vagility can also result in gene flow between otherwise allopatric populations, and in some cases, parapatric or divergence-with-gene-flow models might be more applicable to widely distributed lineages. Here, we use five nuclear introns and the mitochondrial control region along with Bayesian models of isolation with migration to examine divergence, gene flow, and phylogenetic relationships within a cosmopolitan lineage comprising six species, the blue-winged ducks (genus Anas), which inhabit all continents except Antarctica. We found two primary sub-lineages, the globally-distributed shoveler group and the New World blue-winged/cinnamon teal group. The blue-winged/cinnamon sub-lineage is composed of sister taxa from North America and South America, and taxa with parapatric distributions are characterized by low to moderate levels of gene flow. In contrast, our data support strict allopatry for most comparisons within the shovelers. However, we found evidence of gene flow from the migratory, Holarctic northern shoveler (A. clypeata) and the more sedentary, African Cape shoveler (A. smithii) into the Australasian shoveler (A. rhynchotis), although we could not reject strict allopatry. Given the diverse mechanisms of speciation within this complex, the shovelers and blue-winged/cinnamon teals can serve as an effective model system for examining how the genome diverges under different evolutionary processes and how genetic variation is partitioned among highly dispersive taxa.