Thermal collisions between laser excited Xe(nf) Rydberg atoms and a variety of neutral atomic and molecular targets have been investigated. In Xe(nf)-HF collisions, n-changing, 4-changing and collisional ionization were observed. For n = 26 and 27, absolute collisional cross sections for these processes have been determined using time-resolved selective field ionization. In addition, the first evidence of molecular rotational excitation through the transfer of energy of electronic excitation from a Rydberg atom is presented. In Xe(nf) - Xe, Kr, Ar, CO2, CO and N2 collisions the dominant mechanism was observed to be 4-changing: no evidence of n-changing or collisional ionization was apparent. Absolute collisional cross sections have been determined for a range of n between 24 and 37. Comparison of these cross sections with those obtained using a theoretical model in which effects due to the Rydberg core are ignored appears to lead to satisfactory results only for Xe, Kr and CO2, whereas when core effects are included satisfactory agreement between experiment and theory is found in all cases.