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Chemistry in Disks X: The Molecular Content of Proto-planetary Disks in Taurus

(abridged) We used the IRAM 30-m to perform a sensitive wideband survey of 30 protoplanetary disks in the Taurus Auriga region. We simultaneously observed HCO$^+$(3-2), HCN(3-2), C$_2$H(3-2), CS(5-4), and two transitions of SO. We combine the results with a previous survey which observed $^{13}$CO (2-1), CN(2-1), two o-H$_2$CO lines and one of SO. We use available interferometric data to derive excitation temperatures of CN and C$_2$H in several sources. We determine characteristic sizes of the gas disks and column densities of all molecules using a parametric power-law disk model. Our study is mostly sensitive to molecules at 200-400 au from the stars. We compare the derived column densities to the predictions of an extensive gas-grain chemical disk model, under conditions representative of T Tauri disks. This survey provides 20 new detections of HCO$^+$ in disks, 18 in HCN, 11 in C$_2$H, 8 in CS and 4 in SO. HCO$^+$ is detected in almost all sources, and its J=3-2 line is essentially optically thick, providing good estimates of the disk radii. The other transitions are (at least partially) optically thin. Variations of the column density ratios do not correlate with any specific property of the star or disk. Disks around Herbig Ae stars appear less rich in molecules than those around T Tauri stars, although the sample remains small. SO is only found in the (presumably younger) embedded objects, perhaps reflecting an evolution of the S chemistry due to increasing depletion with time. Overall, the molecular column densities, and in particular the CN/HCN and CN/C$_2$H ratios, are well reproduced by gas-grain chemistry in cold disks. This study provides a census of simple molecules in disks of radii $> 200-300$ au. Extending that to smaller disks, or searching for less abundant or more complex molecules requires a much more sensitive facility, i.e. NOEMA and ALMA.