We present a comparative study of the relative abundances of CO, CH3OH, H2CO, HCN, HNC, CS, H2S, CH3CN, SO and HNCO in comets C/1999 T1 (McNaught-Hartley), C/2001 A2 (LINEAR), C/2000 WM1 (LINEAR) and 153P/Ikeya-Zhang, four of the brightest comets seen in 2001–2002. This investigation is based on millimetre/submillimetre observations made with the IRAM 30-m, SEST, CSO and Kitt Peak 12-m telescopes. Although these four comets are expected to originate from the Oort cloud, they present significant differences in molecular abundances, especially as regards to the most volatile species: CO and H2S. In particular comet C/2000 WM1 looks quite depleted in these volatiles, suggesting it may have a different origin than the others. Heliocentric variations of molecular relative abundance in the coma are also investigated. Significant increases in the CS/HCN and HNC/HCN production rate ratios with decreasing heliocentric distances are observed.