Chemistry plays an important role in the structure and evolution of protoplanetary disks, with implications for the composition of comets and planets. This is the first of a series of papers based on data from DISCS, a Submillimeter Array survey of the chemical composition of protoplanetary disks. The six Taurus sources in the program (DM Tau, AA Tau, LkCa 15, GM Aur, CQ Tau and MWC 480) range in stellar spectral type from M1 to A4 and offer an opportunity to test the effects of stellar luminosity on the disk chemistry. The disks were observed in 10 different lines at ~3 resolution and an rms of ~100 mJy beam-1 at ~0.5 km s-1. The four brightest lines are CO 2-1, HCO+ 3-2, CN 2_3-1_2 and HCN 3-2 and these are detected toward all sources (except for HCN toward CQ Tau). The weaker lines of CN 2_2-1_1, DCO+ 3-2, N2H+ 3-2, H2CO 3_03-2_02 and 4_14-3_13 are detected toward two to three disks each, and DCN 3-2 only toward LkCa 15. CH3OH 4_21-3_12 and c-C3H2 are not detected. There is no obvious difference between the T Tauri and Herbig Ae sources with regard to CN and HCN intensities. In contrast, DCO+, DCN, N2H+ and H2CO are detected only toward the T Tauri stars, suggesting that the disks around Herbig Ae stars lack cold regions for long enough timescales to allow for efficient deuterium chemistry, CO freeze-out, and grain chemistry.