Any word can be irregular, but over time the less frequent ones will be forgotten and regenerated by the grammar as regular. You can, if you want an example, look at the history of irregular verbs in English over the last 1000 years or so. As words are used less frequently, they regularize. We don't know exactly what the past or participle forms of "smite" should be, but they're in early versions of the bible and other texts.
More frequent forms are preserved as irregular, and over time they may end up irregular, so eventually this means they probably will be. The verb "be" is irregular in almost every language (I'm thinking about a broad sample, but this is at least literally true throughout Europe), at least if there are any irregular verbs at all.
There's also something similar where "complexity" (=irregularity?) is preserved by small communities with minimal contact with others. Several recent theories about social dimensions of complexity have focused on this, such as work by Trudgill.