  In response to recent chemical attempts to construct higher-spin ladder
materials from organic polyradicals, we study the ground-state properties of a
wide class of antiferromagnetic spin-1 ladders. Employing various numerical
tools, we reveal the rich phase diagram and correct a preceding
nonlinear-sigma-model prediction. A variational analysis well interprets the
phase competition with particular emphasis on the {\it re-entrant phase
boundary} as a function of the rung interaction.
