Mishnah 3 in the chapter of 'Chelek' (Sanhedrin 10:3) is the third of three mishnayos that list those who do not have a share in the World to Come, and it deals with entire groups of people - generations and communities.
The Generation of the Flood:
The first group is the generation of the Flood, who were guilty of robbery and immorality. Regarding them, the mishnah says: "Ein lahem chelek laOlam Haba ve'ein omdin badin" - they have no share in the World to Come, nor will they stand in that great and awesome day of judgment at the end of human history to be judged again. In other words, the punishments they received in the Flood were sufficient, and this is their end.
It should be noted: if there were individuals in these groups who did not deserve this punishment, their judgment would be different. The mishnah is speaking about the generation as a whole, and as we will see, in other cases this is more explicit.
The source for the concept of 'the Great Day of Judgment' - the day when people are judged whether to enter the World to Come and live forever, or to receive further punishment - is in the verses, the most prominent of which is at the end of the Book of Daniel: "And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt" - the multitudes sleeping in the dust will rise, some to eternal life and some to eternal shame and rejection.
The generation of the Flood does not stand even in this judgment, since their suffering was sufficient and there is no reason for them to be judged in order to be punished further. They are considered like the transgressors of the nations of the world, who sin with their bodies, as opposed to the more severe sin of a direct rebellion against God on an ideological and intellectual level. And from where do we know that they will not experience the resurrection of the dead that precedes the World to Come? As it is stated: "My spirit shall not strive with man forever," and the Sages expound the negation as applying to both things at once: neither judgment nor spirit. They will not receive the judgment that precedes the stage of the World to Come, nor will they partake in the spirit of God that the righteous merit in the World to Come.
The Generation of Dispersion:
The second group is the generation of dispersion, the builders of the Tower of Bavel (grammatically it is more accurate to say 'Dor HaPelegah', but it is commonly pronounced 'Dor HaFlagah'). What exactly did they seek to do? The Gemara brings several opinions on this, and the matter is difficult to understand: some say they waged war against God in response to the Flood - whether they intended to fight Him or whether they sought to seal the heavens so that rain would not fall on them again - and some say they built the tower for idol worship. Either way, this was a direct rebellion against God, and therefore it is worse in a certain sense than bodily crimes like succumbing to desires, robbery, and the like.
Therefore, they have no share in the World to Come, as it is stated: "And the Lord scattered them from there upon the face of all the earth" (Bereishis 11:8), and in the following verse: "and from there the Lord scattered them" (ibid., 9). The double reference to scattering comes to teach two separate things: the first - that He scattered them in this world, so that they would not survive in it and would die; and the second - that they were scattered even from the World to Come, so that they will not enter it.
Will they rise to stand in judgment later? There is no mention of this in the text of the mishnah, and Tosafos say that since it does not state that they do not rise, they will certainly rise in the resurrection of the dead and stand for further judgments, since their crime was severe and the punishment they received was not enough to fully atone for it.
The People of Sedom:
The third of the three non-Jewish groups is the people of Sedom, the people of Sedom and Amorah, who were great sinners. They too have no share in the World to Come, as it is stated: "But the people of Sedom were exceedingly wicked and sinful against the Lord." Two expressions are used here: "wicked" - those who distance themselves from God, and "sinful" - those who act against Him, and these are two separate matters: wicked in this world, having turned their backs on God, and sinful regarding the World to Come. However, since their crime was severe and their punishment was not sufficient, "aval omdin badin" - they will stand for further judgment at the resurrection of the dead.
The Dispute Between Rabbi Nechemiah and the Sages:
Rabbi Nechemiah says: "Eilu v'eilu ein omdin badin" - both these and those do not stand in judgment; both the generation of the Flood, the first group, and the people of Sodom, the third group, will not stand for additional judgment at the time of the resurrection of the dead. As it is stated in Psalms: "Therefore the wicked will not rise in judgment, and sinners in the congregation of the righteous." Who are the "wicked" who are not destined to rise in judgment? The generation of the Flood. And who are the "sinners" who do not rise with the righteous to stand in judgment? The people of Sodom, who were called "sinners" in the verse.
But the Sages reject this derivation: "Einam omdim ba'adas tzaddikim, aval omdim ba'adas reshaim" - they do not stand in the congregation of the righteous, but they do stand in the congregation of the wicked; they will indeed not rise with the righteous and will not undergo their judgment process, but they will be resurrected with the rest of the wicked and will stand for the judgment of the wicked, so that they will be judged again.
From here the Mishnah moves on to list groups from within the Jewish people.
The Spies:
The first are the spies - those ten out of the twelve spies who were sent to scout the Land of Israel, and upon their return told the Jewish people that they were unable to enter the land; the nation was convinced by their words, and the result was disastrous. The Mishnah says: "Ein lahem chelek la'Olam Haba" - they have no share in the World to Come.
This provides the strongest proof that when it is said of a certain group that they have no share in the World to Come, there are exceptions: after all, Calev ben Yefuneh and Yehoshua ben Nun are not included among the spies who have no share in the World to Come. From here we see that in the other groups too, there could have been individual exceptions.
And what is the verse that teaches that the spies do not reach the World to Come? As it is stated: "And the men who brought forth an evil report of the land died by the plague before the Lord." "And they died" - in this world; "by the plague" - an additional death, which is the World to Come, and therefore they do not receive an additional punishment afterward and do not merit the World to Come.
And if you will say: The word "plague" comes to explain how they died, in a plague in this world, so how is it expounded? The answer is that had this been the intention, the verse would have said, "And the men died by the plague." Since it first says that they died, and only afterward "the men who brought forth an evil report of the land by the plague," the extraneous word "plague" appearing at the end teaches about another part of the matter - it is the plague that prevents them from entering the World to Come.
The Generation of the Wilderness:
The generation of the wilderness is the generation that lived in the time of the spies and followed their evil counsel and evil attitude, and therefore they died in the wilderness. The spies are worse than them, yet regarding the spies it is not stated explicitly whether they will stand in judgment at the resurrection of the dead; whereas regarding the generation of the wilderness it is stated: "Ein lahem chelek la'Olam Haba v'ein omdin badin" - they have no share in the World to Come and do not stand in judgment, as their punishment was sufficient, and they will not rise to stand trial. As it is stated: "In this wilderness they shall be consumed, and there they shall die" - in this wilderness you shall perish, and there you will remain dead and will not rise again for an additional judgment.
The simple understanding is therefore that the generation of the wilderness was less severe than the spies, who were the ones who stirred up the problem; and therefore the generation of the wilderness does not stand in judgment - they will not stand for an additional trial and an additional punishment later on - whereas the spies do stand in judgment.
This opinion, that the Generation of the Wilderness has no share in the World to Come, is the view of Rabbi Akiva. Throughout the Mishnah here, Rabbi Akiva interprets things to the detriment of the Jewish people, surprisingly and uncharacteristically for him. The Gemara notes that Rabbi Yochanan was astounded that Rabbi Akiva deviated from his usual positive attribute, his way of finding merit and seeing the positive side, and even brings a verse teaching that the Generation of the Wilderness does have a share - the verse in Yirmiyahu where Hashem says, "I remember for you the kindness of your youth... your following Me in the wilderness," the kindness in your leaving Egypt and following Me into the wilderness with faith.
In the Mishnah itself, a Tanna argues with Rabbi Akiva on this exposition: Rabbi Eliezer says that the generation that left Egypt does have a share, as it says in Tehillim, "Gather to Me My pious ones, those who make a covenant with Me over a sacrifice" - gather to Me My pious and righteous ones who made a covenant with Me through a sacrifice, through offerings. For the book of Shemos relates that they brought offerings, and Moshe Rabbeinu sprinkled the blood on them and said that with this, Hashem was making a covenant with them that would be forever. This eternal covenant binds the entire generation with Hashem, and therefore they are included among those who have a share in the World to Come.
The Congregation of Korach:
The next group is the congregation of Korach, the participants in Korach's rebellion. We know that the earth opened its mouth and swallowed them, and we have a tradition that they repented on their way down. The first opinion in the Mishnah is that the men of Korach's congregation will not rise again from the earth that swallowed them to live anew, as it says, "And they and all that was theirs went down alive to the pit, and the earth covered them, and they were lost from the midst of the congregation" - they and all that was theirs went down to the pit, to the grave, and the earth covered them, and they were lost from the midst of the congregation.
Two things were said here: "Vatechas aleihem ha'aretz" - and the earth covered them, this is their end in this world; "vayo'vdu mitoch hakahal" - and they were lost from the midst of the congregation, this is their loss from the World to Come and from their connection to the nation in the future. This too is the opinion of Rabbi Akiva, who holds that they have no future at all.
Rabbi Eliezer argues and brings a verse from the book of Shmuel to prove that the congregation of Korach will receive an opportunity to stand in judgment again for the World to Come: "Hashem brings death and gives life, He brings down to the pit and raises up" - Hashem brings death and gives life and breathes life into the dead, He brings a person down to the pit (the same word as in the previous verse, a reference to the grave) and raises him up from there. And who are those who go down to the pit? This is the congregation of Korach, and Hashem will raise them up again. Thus, they will stand for future judgment, and those worthy of it will even enter the World to Come in the merit of the repentance they did.
The Ten Tribes:
From the Gemara's perspective, this is almost a new Mishnah, and the topic is also new. We are still dealing with groups from within the Jewish people, but here the focus is on the Ten Lost Tribes, and the question is not whether they will reach the World to Come, but whether they will be revealed and return to the main Jewish nation at an earlier stage of history - in this world or in the days of Mashiach - or if they are lost forever.
The Mishnah states: "Aseres hashvatim einan asidin lachzor" - the Ten Tribes who were sent into exile are not destined to return ever. As it says in the Chumash, in the words of Moshe Rabbeinu regarding idol worshippers: "And He cast them into another land, like this day."
What is the meaning of "like this day"? In what way is their casting into a foreign land similar to this day?
Rabbi Akiva, who is strict with the people in this Mishnah as mentioned, expounds: "Mah hayom hazeh holech ve'eino chozer, af hem holchim ve'einam chozrim" - just as this day, once it is over, is over, and it cannot be brought back (and therefore it must be utilized), so too the Ten Tribes went to that other land and are not returning; they are lost forever. These are the words of Rabbi Akiva in understanding the phrase "like this day."
Rabbi Eliezer takes a much more promising and optimistic approach to the verse: "Mah hayom ma'afil uma'ir" - just as every day begins in darkness and later becomes light again, and contains a sort of revelation and redemption from the darkness, "af aseres hashvatim she'afelah lahen - kach asid leha'ir lahen" - so too the Ten Tribes, for whom it is dark, so too it will be light for them in the future. Even though it is dark for them now, as if their sun has set in exile, the sun will eventually rise and shine upon them again: they will be found, returned to the Jewish people, and reunited with them once more.
In summary: This Mishnah listed entire groups that do not have a portion in the World to Come: the Generation of the Flood, the Generation of the Dispersion, and the people of Sodom from the nations of the world, as well as the Spies, the Generation of the Wilderness, and the assembly of Korach from Israel. We noted the distinction between being denied a portion in the World to Come and standing for judgment at the Revival of the Dead, and the disputes among the Tanna'im regarding each of these groups - between Rabbi Nechemiah and the Sages, and between Rabbi Akiva and Rabbi Eliezer. We also saw that individuals such as Yehoshua and Calev are excluded from their group, which implies that there may be exceptions in the other groups as well. At the end of the Mishnah, Rabbi Akiva and Rabbi Eliezer disagreed regarding the fate of the Ten Tribes: whether they are gone and will not return, or whether their sun is destined to shine upon them and they will return.