We consider energy transfer in polymers in dilute solutions and model it as a purely incoherent, hopping exciton motion which ends at permanent traps, whose positions along the polymer chain are fixed. The transport involves not only steps along the chain but also steps between sites which are far away along the chain's backbone but near to each other in Euclidean space. This possibility leads to very peculiar features of the excitation's diffusion along the chain, due to strong correlations between subsequent steps. The process depends strongly on whether the chain is frozen or moves. We show that conformational changes influence trapping strongly, even if they are relatively slow on the time scale of the hopping motion.