The Fall of Samaria is, perhaps, the second most important event for determining the chronology of the Bible. According to 2 Kings 17 and 18, firstly, Shalmaneser V came up to Hoshea of Israel, and that, during this campaign, Hoshea became Shalmaneser’s servant and paid him tribute (2 Kings 17:3). However, in 2 Kings 17:4, Shalmaneser put Hoshea in jail due to the fact he had paid no tribute. Shalmaneser conducted three known campaigns in his reign: one in 725 BC, one in 724 BC, and one in 723 BC. He did not conduct a campaign in 726 BC. It seems that the payment of tribute during Shalmaneser’s first campaign and the rebellion are extremely unlikely to have taken place in the same year. Since Samaria was besieged in Hoshea’s seventh year (2 Kings 18:9) and fell in his 9th, and since Tiglath-Pileser III records tribute from Hoshea in 731 BC, the only logical conclusion is that Hoshea (using accession-year dating), seized power between the spring and summer of 731 BC (Israel began its new year in spring), immediately paid tribute to the great Tiglath-Pileser, then, paid tribute to Shalmaneser in 725 BC (his 6th year), then, in 724 BC, revolted, forcing Shalmaneser, as in 2 Kings 18:9, to come up against Samaria and besiege it for three years, Samaria falling in Hoshea’s 9th year, 722 BC. The date of the Fall of Samaria, is, logically, 722 BC.
UPDATE: I now renounce the above reasoning in favor of Galil’s view. I also now view Hoshea’s accession as stemming from Tiglath Pileser’s Galilee campaign of 732 BC, making the above reasoning needless, the fall of Samaria being in 732 BC.
UPDATE (4/20/2013): I now view Hoshea’s accession as being sometime in the winter of 732-31 and not as stemming from Tiglath Pileser’s Galilee campaign. The above reasoning is still needless.