Appropriately enough, it is the loathsome Antinous who's first to get his comeuppance—and a richly deserved comeuppance at that. Antinous is the unofficial leader of Penelope's suitors, eating Odysseus out of house and home while they pester his wife for her hand in marriage. Antinous is by far the most arrogant and disrespectful of all the suitors. Not only does he disrespect Odysseus by courting his wife, he also plans to murder Telemachus upon his return to Ithaca. Worse still, he throws a stool at Odysseus when he returns to the palace disguised as a beggar.
One thing we must always bear in mind is that Odysseus is a king, and this is his palace. It's not possible for anyone to have behaved as disrespectfully towards Odysseus as Antinous has done. By the standards of the time, and not just in ancient Greece, he has committed the very highest of high treason. As such, when his inevitable end finally comes, it is more than simply poetic justice that is meted out by Odysseus's arrow.