Japanese verb conjugation is very regular, as is usual for an agglutinative language, but there are a number of exceptions. The best-known irregular verbs are the common verbs する suru "do" and 来る kuru "come", sometimes categorized as the two Group III verbs. As these are the only significantly irregular verbs, and the only verbs frequently flagged as irregular, it is sometimes incorrectly stated that these are the only irregular verbs in Japanese, but there are in fact more, about a dozen total, depending on how one counts. The other irregular verbs encountered at the beginning level are ある aru "be (inanimate)" and 行く iku/yuku "go", with the copula behaving similarly to an irregular verb.
There are also a few irregular adjectives, of which the most common and significant is 良い yoi "good".
The most significant irregular verbs are the verbs する suru "do" and 来る kuru "come", which are both very common and quite irregular. Often the conjugations behave as if they were instead the verb しる or す, or respectively きる or こる, where (other than す) these are vowel stem ("Group II", 1-row, monograde) conjugation (note that there are no -oru vowel stem verbs, though 来る sometimes behaves as if it were one), but beyond there are further exceptions. Historically する came from earlier す, which explains some of the irregularity. The following table is ordered to emphasize the regularities.
The irregular 〜ない -nai stem of する is often overlooked; it is used in grammatical forms where the 〜ない form is used without the 〜ない – generally formal – as in 食べず tabe-zu "without eating" or 食べんがため tabe-n ga tame "for the purpose of eating". In these contexts する becomes せ, as in せず se-zu "without doing" or せんがため se-n ga tame "for the purpose of doing". Note the similarity to 〜ません as the negative form of 〜ます, of the same origin.
The potential 来れる koreru form is from the omission of ra in the られる rareru potential form, and is found in all Group II verbs; it is considered an error by prescriptive grammarians, but is increasingly common, particularly in spoken speech and in younger Japanese.
The copula だ and です (polite), together with the verb ある aru "be (inanimate)", which is used grammatically, and the 〜ます suffix, which functions similarly to an irregular auxiliary verb, are all irregular to varying degrees, and particularly used in polite speech. It is debatable whether they should be classified as verbs or as different parts of speech.