Whilst searching for the origin of irregular verbs, I came across this forum, which points out, among other things, that irregular verbs are more often than not common words. Is there a reason for this? And why does this happen more in some languages than others? (Also mentioned on the forum).
The forum linked to in the question provides the key points that answer the question. Irregular forms like those asociated with irregular verbs occur frequently in a language. They have to occur frequently because if they did not, they would disappear, becoming regular.
A vivid example of this principle is provided by the strong verbs in Germanic languages (which includes English). The strong verbs are irregular in their conjugation pattern, e.g.
sing-sang-sung run-ran-run eat-ate-eaten stand-stood-stood keep-kept-kept
Strong verbs like these, with their irregular conjugation patterns in terms of a stem vowel change, denote everyday actions. This is important because it means that they occur frquently in everyday communication. The conjugation of weak verbs, in contrast, is regular, e.g.
work-worked-worked lift-lifted-lifted move-moved-moved place-placed-placed study-studied-studied
The strong verbs often experience a stem vowel change in their simple past and past participle forms, whereas the weak verbs consistently build these forms with the -ed inflectional suffix.
The number of strong verbs in a Germanic language is relatively small, just about two hundred in English and German. The number of weak verbs, in contrast, is huge, in the thousands. Every new verb that enters the language is weak, e.g. google-googled-googled, skype-skyped-skyped. What this means is that the pattern for weak verbs is productive and alive in the language. The pattern for strong verbs, in contrast, is dead and frozen.
In the history of Germanic languages, the conjugation of strongs verbs, which often involves a stem vowel change, is much older than the pattern for weak verbs, which, again, involves the -ed suffix. At some point in the development of Germanic, the pattern for weak verbs entirely replaced the pattern for strong verbs. The pattern for strong verbs simply died.
The frequent occurrence of a strong verb is essential for maintaining its status as a strong verb. There are a few strong verbs in English that are in flux, i.e. they are becoming weak verbs. This can be said of, for instance, hang, e.g. I hung it up vs. I hanged it up, It hung on the wall vs. It hanged on the wall. The other day I came across the form slided; I had to stop and ponder whether that was correct or incorrect, e.g. It slid down the hill vs. It slided down the hill. With strong verbs that occur really frequently, in contrast, there is no hesitation for me, e.g. He ate it vs. *He eated it, She ran to the store vs. *She runned to the store. Strong verbs like eat and run occur frequently enough that our sense of the correct form is robust. The strong verbs hang and slide, in contrast, occur less frequently and as a result, they are tending in the direction of the productive pattern of weak verbs.
The term paradigmatic leveling denotes the greater phenomenon. The paradigma (i.e. the conjugation pattern of verbs or declension patterns of nouns) associated with the words in question is "leveled", meaning that it becomes regular.