Recent experiments on rapid neutral-neutral reactions involving the radical CN at low temperature and the neutral C atom at room temperature suggest that atom-neutral and radical-neutral reactions may be generally more rapid at low temperature than hitherto thought. We have included a variety of rapid neutral-neutral reactions in our gas-phase chemical models of quiescent, dense interstellar clouds. We find the calculated abundances of many molecules to be greatly changed from previous values. In particular, the peak 'early-time' abundances of organic molecules are reduced.