We study the effects of Ar+, He+ and C+ ion irradiation on multi-walled carbon nanotubes at room and elevated temperatures with transmission electron microscopy (TEM) and Raman spectroscopy. Based on the TEM data, we introduce a universal damage scale for the visual analysis and characterization of irradiated nanotubes. We show for the first time that the amount of irradiation-induced damage in nanotubes is larger than the value predicted for bulk materials using the simple binary collision approximation, which may be associated with higher defect production due to electronic stopping in these nanoscale systems. The Raman spectra of the irradiated samples are in qualitative agreement with the TEM data and indicate the presence of irradiation-induced defects. However, it is difficult to obtain quantitative information on defect concentration due to non-uniform distribution of defects in the nanotube films and in part due to the presence of other carbon nanosystems in the samples, such as graphitic crystallites and carbon onions.