While most rivers and lakes follow predictable principles of hydrology and geology, a few defy the rules. Some rivers diverge rather than converge; some rivers flow two directions; some lakes have not one but two outlets; some watersheds have ambiguous boundaries. The scientific literature on these exceptions is sparse, scattered, and, in some cases, conflicting. We provide an authoritative overview of nine unusual natural drainages in North and South America, including river bifurcations and bifurcation lakes: Casiquiare River, Arroyo Partido, Wayambo River, Atchafalaya River, North Two Ocean Creek, Divide Creek, Committee’s Punch Bowl, Echimamish River, and Wollaston Lake. Most instances are found on flatlands and saddles. Some watershed boundaries are still unresolved or even dynamic, suggesting river formation in progress. We discuss the exploration, geophysical settings, hydrology, ecology, use, and management of these extraordinary drainages.