  We present Submillimeter Wave Astronomy Satellite (SWAS) observations of the
1_{10}-1_{01} transition of ortho-water at 557 GHz toward 12 molecular cloud
cores. The water emission was detected in NGC 7538, Rho Oph A, NGC 2024, CRL
2591, W3, W3(OH), Mon R2, and W33, and was not detected in TMC-1, L134N, and
B335. We also present a small map of the water emission in S140. Observations
of the H_2^{18}O line were obtained toward S140 and NGC 7538, but no emission
was detected. The abundance of ortho-water relative to H_2 in the giant
molecular cloud cores was found to vary between 6x10^{-10} and 1x10^{-8}. Five
of the cloud cores in our sample have previous water detections; however, in
all cases the emission is thought to arise from hot cores with small angular
extents. The water abundance estimated for the hot core gas is at least 100
times larger than in the gas probed by SWAS. The most stringent upper limit on
the ortho-water abundance in dark clouds is provided in TMC-1, where the
3-sigma upper limit on the ortho-water fractional abundance is 7x10^{-8}.
