title_body: What verbs should be irregular in a naturalistic conlang?
upvoted_answer: The first class of verbs that is often highly irregular are the auxiliary verbs. This does not only comprise to be and to have but also the modal auxiliaries (like must, can, shall, and will). They are used very frequently and tend to erode phonetically, and they are also prone to suppletion (showing a mixture of different stems from originally different words).
  
  A quick check (for my native language German) seems to confirm your intuition that verbs of motion are more often irregular than average. They are also used quite frequently. In Romance languages, the basic verb for to go (e.g., French aller or Italian andare) is very irregular and mixing several different stems ((vulgar) Latin ambulare/allare, vadere, ire).
  
  Some verbs are irregular because they rhyme with an irregular verb, e.g., German schreiben, schrieb, geschrieben "to write", borrowed from Latin scribere, became irregular because of rhyming verbs like bleiben "to stay".