The verb gleiten has past and perfect forms
glitt, hat geglitten
Entgleiten is also irregular, with the same forms
entglitt, ist entglitten
But begleiten is regular:
begleitete, hat begleitet
The Duden entry of begleiten says
Herkunft
Vermischung von gleichbedeutend veraltetem beleiten (mittelhochdeutsch beleiten, althochdeutsch bileiten) mit ↑geleiten
It seems that the reason why begleiten has a different past and perfect forms than gleiten is that it is not derived from gleiten, but rather a mix of beleiten and geleiten.
What are some other examples of verbs that have different past/perfect forms than their (apparent) roots? How common is this phenomenon?