In several Germanic languages (at least German & Danish; to the best of my knowledge it has more or less died out in the modern English and Norwegian languages), verbs broadly termed 'motion verbs' (generally those expressing change of state or position) will take 'to be' as their auxiliary when used intransitively, that is, without a direct object. This is superficially similar to but quite not as arbitrary as the 14 French verbs which take être as an auxiliary.
Focusing on how this manifests itself in Danish, there are two main subgroups of verbs which can be used with either 'have' or 'være'. For some of these, this can be attributed to a transitive usage (is something happening to sth?): Der er kørt en bil i vandet 'A car has driven into the water' ; Compare this with intransitive usage (is something just happening?): Jeg har kørt bil i mange år 'I have driven/been driving (a car) for many years'.
For a second group, The Danish Comprehensive Grammar classifies an action is being done in the past (perhaps seen as a process?): Han har gået 10 kilometer 'He has walked 10 kilometres' ; or as expressing a state (seen as a result?) : Nu er han gået 'Now he has gone/left'. Furthermore, this last one is not to be confused with 'He is gone' Han er væk.
In summary, I am yet to find a complete list anywhere, but generally all verbs of moving/driving/flying/swimming/etc as well as at blive, at begynde (but not at være for any German speakers) will form their past compound tenses with at være, IF they are used intransitively.
I can't find a complete list but I think var is used only for some verbs. This list is pretty arbitrary (at least from layman's perspective) and the only characteristic that somehow groups the verbs together is their relationship to movement. However it doesn't mean the inverse - that all verbs that have something to do with movement use it.
I think it is similar to French which uses avoir/être where être is used only with 17 verbs including aller (go), entrer, arriver but also rester, naître (be born) or mourir (to die). The movement aspect of the verbs is a pretty weak connection but it can be useful nonetheless.