Chances are, your Sunday School Bible stories glossed over that salient detail. As you may recall, the Israelites prevail upon the prophet Samuel against his better judgment to give them a king, as all the nations around them had. It is not Samuel, however, but God who chooses Saul as king:
[Saul and his servant] went up to the city; and as they entered the city, there was Sh’mu’el [Samuel] coming out toward them to go up to the high place. The day before Sha’ul [Saul] arrived, Adonai [The Lord] had given Sh’mu’el a revelation: “Tomorrow at about this time I will send you a man from the territory of Binyamin [Benjamin]. You are to anoint him prince over my people Isra’el. He will save my people from the power of the P’lishtim [Philistines], because I have seen my people’s situation, and their cry of distress has come to me.” When Sh’mu’el saw Sha’ul, Adonai said to him, “Here is the man I told you about, the one who is going to govern my people.” (1 Samuel 9:14-17, Complete Jewish Bible)(I like the CJB for Old Testament references, just to avoid the influence of medieval Christian translators.)
So, God had at first been so impressed with Sha’ul/Saul, and you probably remember that Saul did something or other that displeased God so much that God sent Samuel out to find someone outside of Saul's family to anoint as the next king. Samuel finds Jesse and determines to check out each of Jesse's boys, finding each of them unsatisfactory until someone goes and fetches David in from herding the family's sheep. Samuel anoints David Heir Apparent, and David goes on to slay Goliath and ten thousand more Philistines.
But what did Saul do that was so wrong? Well, there was the matter of going ahead and attacking the Philistines -- and more importantly, making the prerequisite burnt offering himself instead of waiting over a week for Samuel to show up to do it.
Sh’mu’el said to Sha’ul, “You did a foolish thing. You didn’t observe the mitzvah of Adonai, which he gave you. If you had, Adonai would have set up your kingship over Isra’el forever. But as it is, your kingship will not be established. Adonai has sought for himself a man after his own heart, and Adonai has appointed him to be prince over his people, because you did not observe what Adonai ordered you to do.” (1 Samuel 13:13-14 CJB).
But the last straw, Saul's damning offense, comes after Saul and his son Jonathan have driven the Philistines away. Samuel returns and tells Saul that God wants him to commit genocide against another of the Israelites' neighbors, the Amalekites.
[Samuel said,] "Here is what Adonai-Tzva’ot says: ‘I remember what ‘Amalek did to Isra’el, how they fought against Isra’el when they were coming up from Egypt. Now go and attack ‘Amalek, and completely destroy everything they have. Don’t spare them, but kill men and women, children and babies, cows and sheep, camels and donkeys.’” (1 Samuel 15:2-3, CJB)The reason God was supposed to be so angry at the Amalekites was that way, way back centuries earlier when the Israelites were wandering the desert with Moses and Joshua, Amalekites attacked them from the rear. The Israelites had no shortage of hostile neighbors (see 1 Samuel 14:47), but their -- I mean, of course, God's -- grudge against the Amalekites runs hysterically deep. Three of the 613 mitzvot (commandments) from the Old Testament are to remember what the Amalekites did to Jews, not to forget what the Amalekites did to Jews, and to destroy the Amalekites utterly (Deuteronomy 25:17–18, Exodus 17:14 and 1 Samuel 15:3.)
Saul, however, took the king of the Amalekites captive instead of killing him, and his troops didn't kill every one of the sheep and cattle outright. Samuel pronounced God's final judgment against Saul, and cut the chained king of the Amalekites into pieces.
The History Channel version sanitizes this chapter as much as it can without rewriting the basic plot. Yes, Samuel tells Saul to kill every last one of the Amalekites, but what we see is a small encampment of maybe five or six tents, and there is not one woman, child, or baby to be seen. Slaughter ensues, but it barely qualifies as genocide.
Oh, and Samuel merely slits King Agag's throat rather than going into a Tarantino-esque orgy of gratuitous gore.