These everyday verbs have another feature: they have been in the English language for a long time. The oldest verbs were ones that were borrowed from other languages, or have come into English from Old English, before the patterns of regular conjugation were formed.
Consider to go and its past tense went. The following is from http://www.etymonline.com/index.php?term=go.
Old English gan "to go, advance, depart; happen; conquer; observe," from West Germanic *gai-/*gæ- (cf. Old Saxon, Old Frisian gan, Middle Dutch gaen, Dutch gaan, Old High German gan, German gehen), from PIE *ghe- "to release, let go" (cf. Sanskrit jihite "goes away," Greek kikhano "I reach, meet with"), but there is not general agreement on cognates.
The Old English past tense was eode, of uncertain origin but evidently once a different word (perhaps connected to Gothic iddja); it was replaced 1400s by went, formerly past tense of wenden "to direct one's way" (see wend). In northern England and Scotland, however, eode tended to be replaced by gaed, a construction based on go. In modern English, only be and go take their past tenses from entirely different verbs.
So how did went become the past tense for go?
The etymology indicates that it probably came from the past tense of wenden.
The verb to get has a similar Old English pedigree.
Contrast these ancient verbs with newly-coined, modern verbs. The modern verbs will always be regular. For example, You gross me out. / You grossed me out. / You are grossing me out.
Or imagine that you are coining a new verb, for example, to smurf, meaning to pelt with a blue doll. You would undoubtedly come up with a regular construction, namely I smurf proudly. / I smurfed when I was younger. / Your smurfing is becoming tiresome.
Contrast the Old English verbs with verbs that have been repurposed. To fly is an Old English verb and it is correct to say, I flew out of Atlanta. But watch what happens when you use the verb to fly in baseball. When a batter hits a ball to the outfield and it is caught, the ball is called a fly ball and the play is called a fly out. The next time he comes to bat, the announcer will usually say he flied out. This modern usage of an old verb follows a regular construction: He flies out. / He flied out.
Please take a look at this list of about six hundred regular English verbs. Contrast with the much shorter list of irregular verbs. Although both lists have everyday verbs, it seems that the largest factors are when and through which language they entered Modern English.