In 2003-2005 seven comets were investigated at millimeter to submillimeter wavelengths using CSO and IRAM-30m facilities: C/2002 V1 (NEAT), C/2002 X5 (Kudo-Fujikawa), 2P/Encke, C/2002 T7 (LINEAR), C/2001 Q4 (NEAT), C/2004 Q2 (Machholz) and 9P/Tempel 1. With these observations, we can further extend our comparative study of the molecular composition of comets (Biver et al. 2002, EMP 90, 323) and improve our understanding on the evolution of molecular abundances with heliocentric distance (rh) (between rh = 0.1 and 2.8 AU from the Sun). The sample is also very diverse, with comets of the shortest (3.3 years) and long orbital period: 9000 to 30 million years. A total of 12 molecules: HCN, CH3OH, CS, CO, H2CO, H2S, HNC, CH3CN, SO, HNCO, HC3N and HCOOH were observed and detected in at least one comet, in some cases for the second time since their identification in comet Hale-Bopp in 1997. We present our main results, including the following findings: (1) The HNC/HCN production rate ratio appears to plateau at a maximum value around 0.2 for rh < 0.5 AU, after initially increasing with decreasing heliocentric distance; (2) The CH3OH/HCN ratio, on the other hand, seems to decrease towards the Sun, as observed in C/2002 X5 and C/2002 T7; (3) HDO was searched for in C/2004 Q2 (Machholz) and the upper limit obtained for the D/H ratio in water (< 0.00023; 3-σ ) is lower, though only marginally, than the value of 0.0003 measured in other long period comets; (4) Both comets 2P and C/2002 T7, the comets having the shortest and longest orbital periods among the sample, have a high methanol abundance (about 4% relative to water). The abundances of all molecules detected and searched for are presented and a comparison between comets, including comet Hale-Bopp, is shown.< Leer menos