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The term nasality refers to the timbre of the nasal phonemes. It is also used to express the quality of sound that characterises some speakers. In this paper, we propose to classify nasality in natural speech into four types: phonemic nasality, nasality in assimilation, incidental nasality in the production of voiced plosives, and nasality associated with speaker individuality. Speech sounds recorded separately for oral and nasal outputs were analysed and the four types of nasality were observed individually. In order to investigate the relationship between the nasality in running speech and the perception of speaker similarity, we conducted an experiment. The results revealed that listeners rated speaker similarity exploiting phonemic nasality when it existed in the utterance and also used speaker-related nasality regardless of the existence of phonemic nasals.