Indeed, cremation was not the accepted burial rite in Ancient Israel, and this was definitely an unusual practice by Israelite standards and almost unheard of in the ANE (The only people known to practice cremation were the Hurrians and the Hittites), so this must have been an exception to the rule, see here. However, this author believes that it may have been accepted practice for Israelite royalty.
The IVP Bible Commentary suggests that Saul's body may have been so badly dismembered and in an advanced state of deterioration that the corpses required extreme measures to purify it, and no embalming techniques would have been effective at this point.
There are other suggestions which are unlikely; namely, that Saul's corpses were not cremated but incense was burnt for the corpses (cf. 2 Chro. 6:14; Jer. 34:5), or that they were smeared with spices, see here. However, it has to be noted that there is a big difference between Saul's burning and the burnings of Israelite kings mentioned elsewhere in the bible. In Chronicles for example, Asa's body was clearly not cremated but incense were burnt in his honor, this is evident from the Hebrew וישרפו לו, "they burnt for him", or "in his honor". In Jeremiah similarly it is ישרפו לך which is 'to you'. But in Samuel we find וישרפו אותם, which clearly denotes "burnt them" or "their corpses"; thus it is hard to escape the conclusion that Saul's corpses were cremated by the inhabitants of Jabesh-Gilead. It is my opinion that this was not common procedure in ancient Israel even for royalty, and that this was an extreme measure; it is likely that this was done because of the deteriorated and shameful state of their corpses.