We present Submillimeter Wave Astronomy Satellite (SWAS) observations of the 110 → 101 transition of ortho-H2O at 557 GHz toward 12 molecular cloud cores. The water emission was detected in NGC 7538, ρ Oph A, NGC 2024, CRL 2591, W3, W3OH, Mon R2, and W33 and was not detected in TMC-1, L134N, and B335. We also present a small map of the H2O emission in S140. Observations of the H218O line were obtained toward S140 and NGC 7538, but no emission was detected. The abundance of ortho-H2O relative to H2 in the giant molecular cloud cores was found to vary between 6 × 10-10 and 1 × 10-8. Five of the cloud cores in our sample have previous H2O detections; however, in all cases the emission is thought to arise from hot cores with small angular extents. The H2O 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-H2O abundance in dark clouds is provided in TMC-1, where the 3 σ upper limit on the ortho-H2O fractional abundance is 7 × 10-8.