The past tense of the verb 'to run' is 'ran'. In English, regular verbs typically follow the pattern of adding '-ed' to form the past tense, but 'run' is an irregular verb and does not follow this rule. Instead, the past tense is formed by changing the vowel from 'u' in 'run' to 'a', making it 'ran'. This is a common trait among irregular verbs, where the past tense form differs significantly from the base form.