Does the verb ver have a stem change because it is conjugated mostly regularly? I mean that the stem is ve- when it would normally be v-. Just curious.
Ver comes from Latin vidēre, with conjugated forms like videō "I see" (1st person singular present tense). Latin short /i/ turned into Spanish /e/, while unstressed /eo/ usually gave /io/. So at some point this must have been vedio [be.ði.o], with the middle /d/ softened to [ð] (as in English this).
The vowels in hiatus were turned into diphthongs, so disyllabic [i.o] became monosyllabic [jo] (as in English yo or yaw); this was and is still a common tendency in Spanish.
The middle [ð] (between vowels) was lost in a lot of words in Spanish, or turned into [j] or merged with a following [j]. So we find medieval Spanish spellings like veyo [be.jo]. The infinitive was either veer or veyer according to dialect (the latter still exists in Aragonese). Other tenses didn't get this [j] sound.
In time the verb was regularized and the forms with -y- lost it.
Finally, because the speakers' intuition said that the root was v- and not ve-, and because Spanish doesn't like vowels in hiatus (and least of all pairs of identical vowels), veer was simplified to ver. Only the imperfect retained the ve- root.
More or less the same happened to ser, which was formerly seer, from Latin sedēre "I sit, I remain". I didn't happen with leer because... well, just because.
Parts of this process also happened with traer, caer, oír and other verbs where the loss of middle consonants got two vowels in contact. You can still see the middle -y- in the preterite, 3rd person plural (cayeron, oyeron), and a different "solution" to the problem in the present, 1st person singular (traigo, caigo, oigo).