Mishna: Achav {Ahab} Has No Share in the World To Come

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Achav had some merits. He was a war hero. He gave honor to the Torah and some Torah Scholars gained benefits from his property. He allowed Eliyahu to slaughter the priests of idolatry at Mount Carmel. On at least 2 occasions he showed some degree of Teshuva.
Nevertheless the main view of the rabbis in the Talmud (although there is a dissenting view) is that he does not have a share in the world to come.
http://www.ou.org/torah/tt/5765/vayechi65/navi.htm

Three Kings Do Not Have a Share in the World To Come (Divrei HaYamim Bet 33:12-17, Sanhedrin 101b-102b)
In the course of discussing these verses in Chronicles that describe the teshuva of Menashe, the Talmud analyses the actions of the three most evil kings in the Tanach. Yeravam ben Nevat never repented and so forfeited his share in the World to Come. However the other two actually did teshuva and therefore their punishment is more problematical.

The very name Achav tells us that he was an 'ach' a brother who was born to be an enemy and 'av' a father to idolatry. His most trivial deed was like the sins of Yeravam, yet he refused to hand over the Torah, his most precious possession, when demanded to by Ben Hadad, king of Aram. His father Omri merited fathering four generations of kings in Israel by adding a new town Shomron, [that the Romans later called Sebastia and lies close to Shechem] whereas Achav's merit that earned him generations of kingship was his support and respect for Torah scholars.

Furthermore, when rebuked by Eliyahu for the murder of Navot and then stealing his vineyard, Achav repented and Hashem postponed the destruction of his dynasty, till after the death of his sons. So Rav Nachman said that Achav's evil deeds were actually balanced by his good ones. However, Rav Yosef objected to this since of Achav we are told "And he did evil in the sight of the Lord more than any before him" (1 Kings 16:30). This is evidenced by Jezebel his wife, who every day weighed Achav and donated his weight in gold to avoda zara. Perhaps the consequences of Navot's murder would have been even more serious so that his teshuva would not have availed to postpone the punishment were it not for the deceit by the spirit of Navot. When Hashem called for somebody to cause Achav to go to the war with Ben Hadad in which he was mortally wounded, the spirit volunteered, "I shall be a lying spirit in the mouth of all [Achav's] prophets [who will prophesy victory over Ben Hadad] " (Melachim Alef 22:21-22). Because of this, Hashem, "before whom one who lies cannot remain in His Presence" (Ps. 101:7), while allowing the spirit of Navot to draw Achav into battle, dismissed the spirit from His Presence and retained the postponement of the punishment on Achav's dynasty. However, despite his teshuva, there was something that denied Achav of the World to come. Said Rabbi Yochanan, "Achav wrote on the doors of Shomron, 'Achav has denied the G-d of Israel', so he has no share in the World to Come".

There might be an additional reason, he has no share in the World to Come (according to the Mishna), besides what he wrote on the doors of Shomron.
Bli neder, I, G-d willing, would like to comment about this on another occasion.

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The following is an online translation of Rambam's Hilchot Teshuva 3:6
http://www.panix.com/~jjbaker/MadaT.html

6) The following types of people have no share in the World to Come, and are cut off, destroyed and excommunicated for ever on account of their very great sins and wickedness: An infidel; a heretic; one who denies the Torah; one who denies that there will be a Resurrection; one who denies that there will be a Redemption; one who converts from Judaism; one who causes a lot of people to sin; one who withdraws from communal ways; one who publicly sins in a defiant way like Jehoiakim did; an informer [against Jews]; one who instills fear in the congregation but not in the Name of God; a murderer; one who relates loshan ho'rah; and one who pulls back his foreskin [in order to cover his brit milah].

Achav was not only guilty of ideological sins. He was a murderer.

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In II Melakhim/Kings 9:7 the prophet instructs Yehu the son of Yehoshafat the son of Nimshi (see there, 9:2) to destroy the household of Achav. As it says (Jerusalem Bible's translation):

"And thou shalt smite the house of Ah'av thy master, that I may avenge the blood of my servants the prophets, and blood of all the servants of the L-rd at the hand of Izevel".

Here the emphasis is on Achav's role in spilling the blood of the righteous as his chief crime at least as far as G-d taking vengeance against him in this world. However, it is reasonable to say that this was also a major factor according to the Mishna in causing Achav to lose his share in the world to come.

But I won't hide one weakness in the proof. Namely, when one kills the prophets and the servants of G-d, he is also harming the nation on the spiritual level and not just on the physical level. So we still need the Rambam that I quoted earlier as definite proof that murder of the righteous can cause someone to lose his share in the world to come.