Magnetization and neutron diffraction measurements indicate long-range antiferromagnetic ordering below TN=4 K in the 2D, S=1/2 Heisenberg antiferromagnet K2V3O8. The ordered state exhibits ``weak ferromagnetism and novel, field-induced spin reorientations. These experimental observations are well described by a classical, two-spin Heisenberg model incorporating Dzyaloshinskii-Moriya interactions and an additional c-axis anisotropy. This additional anisotropy can be accounted for by inclusion of the symmetric anisotropy term recently described by Kaplan, Shekhtman, Entin-Wohlman, and Aharony. This suggests that K2V3O8 may be a very unique system where the qualitative behavior relies on the presence of this symmetric anisotropy.