We show that in an optical trap the ground states of spin-1 bosons suc
h as Na-23, K-39,and Rb-87 can be either ferromagnetic or ''polar'' st
ates, depending on the scattering lengths in different angular momentu
m channels. The collective modes of these states have very different s
pin character and spatial distributions. While ordinary vortices are s
table in the polar state, only those with unit circulation are stable
in the ferromagnetic state. The ferromagnetic state also has coreless
(or Skyrmion) vortices like those of He-3-A. [S0031-9007(98)06714-3].