King Saul was as different from others in righteousness, as black is from white: Moed Katan 16b
King Saul as one of the 8 "Princes" - Yishai, King Saul, Samuel, Amos, Tzefaniah, Tzidkeyahu/Chizkeyahu, Messiah, Eliyahu: Succah 52b
Rachel's protection of Leah, by giving her the signs which Ya'akov and she had established, was rewarded by having King Saul as her descendant: Megillah 13b
King Saul's modesty, in hiding his new status as King, was rewarded by having Esther as his descendant: Megillah 13b
King Saul's neck was modeled on the Divine in that it was greater than the physical norm, and this was the area in which he ultimately was hurt: Sotah 10a
King Saul was anointed from a pitcher of oil, King David and King Shelomo from horns of oil: Megillah 14a
King Saul reigned for three years, one of which was together with Samuel: Temurah 15a
King David descended to the core of his learning, and merited, "Those who have of You see my and are glad." King Saul did not, and so "Where he turned he created evil.": Eruvin 53a
The Army
The soldiers' special Bill of Divorce (as performed by King David's Brothers): Ketuvot 9b