  Vortex states of weakly-interacting Bose-Einstein condensates confined in
three-dimensional rotating harmonic traps are investigated numerically at zero
temperature. The ground state in the rotating frame is obtained by propagating
the Gross-Pitaevskii equation for the condensate in imaginary time. The total
energies between states with and without a vortex are compared, yielding
critical rotation frequencies that depend on the anisotropy of the trap and the
number of atoms. Vortices displaced from the center of nonrotating traps are
found to have long lifetimes for sufficiently large numbers of atoms. The
relationship between vortex stability and bound core states is explored.
