The stacks of Bose-Einstein condensates coupled by long Josephson junctions present a richphenomenology feasible to experimental realization and specially suitable for technologicalapplications as the nonlinear-optics and superconducting analogs have already proved. Among this,we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates cancarry tunneling superflows whose dynamical stability depends on the quasimomentum. Across thestacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yieldtransverse Josephson vortices with a generic non-integer circulation in units ofh/m. Additionally, thesuperpositions of degenerate linear Bloch waves can suppress the supercurrents and give rise tofamilies of nonlinear standing-wave states with strong(transverse)spatial localization. Stable states ofthis type can also be found infinite size systems.