In later, more localized adaptations of Buddhism, there are many hells, or Narakas, where those who racked up particularly bad karma were reborn, where they live, suffer, die, and are reborn again for many kalpas (eons) on end until they have worked off all their bad karma. But the lowest hell, Avici, is reserved for those who commit one or more of the Five Grave Offenses, the personal Moral Event Horizons of the religion: intentionally murdering one's father, intentionally murdering one's mother, killing an arhat (enlightened being), shedding the blood of a Buddha, and causing a schism in the sangha (the community of Buddhist monks and nuns). Existence in the Avici hell lasts the longest out of all of the other hells put together, such that it is often known as "the non-stop way."
The crimes listed are so terrible that it is very rare for a Buddhist monk to publicly condemn a man to Avici, as it's a serious accusation that could be seen as Malicious Slander if proven untrue.
Avici means "without waves". One can translate it to The Ceaseless. With a cosmology where a trillion of trillion years is a mere metric for time, this should clarify that the cosmic judgment of karma reserves Avici for the most vile only.
Also, considering the cyclic nature of Buddhist cosmology, even sins fit for Avici are not truly irredeemable. Still, that is only theoretical. Nobody who has fallen into Avici, since the beginning of reality an infinity years ago, has been redeemed yet.
However, there is dispute about when this idea originated. Traditionally, it comes from the story of Devadatta, a monk who killed his father, twice assaulted the Buddha, and split the sangha. But there are at least two versions of the story of Devadatta — one of which has him being consigned to a very long stay in Avici and one of which has him repenting and achieving some level of enlightenment. Some historians date the story of Devadatta to a hundred years or more after the Buddha died, which would make it a later addition.
In Classical Mythology, you can do almost anything — including murder and rape — and still be considered a hero, but there are three exceptions, and any hero who committed one of these three sins would lose their title: Hubris, impiety, and violation of xenia.
Tantalus committed all three of the above sins while also cementing two more acts as among the worst taboos in Greek Mythology: cannibalism and murdering your offspring. Tantalus killed his son, cooked him, and tried to feed him to the Greek gods, succeeding with Demeter. Tantalus did all this just to prove himself better than the gods. By killing his own son, and making one of the gods an unwitting cannibal, Tantalus became one of the worst humans in Greek Mythology.
Athena and Poseidon both crossed it in one version of Medusa's origin: Poseidon raped Medusa, and Athena punished Medusa for the "crime" of having sex with a god by turning her and her sisters into ugly monsters. Athena later mocked Medusa's death.
Hera crossed it by making Hercules kill his family.
Like Tantalus, Ixion committed all three of Greece's taboo crimes. First, he violated xenia by throwing his father-in-law into a pit of hot coals when the latter was visiting. Then, Ixion went to Mount Olympus to beg Zeus, whose job it is to punish violators of Xenia, for his crime, for forgiveness. Surprisingly, Zeus agreed to do so. Ixion then committed hubris by being an Ungrateful Bastard towards Zeus and lusting after Hera. Finally, he arguably committed impiety by attempting to sleep with Hera, although he only slept with a duplicate that Zeus made out of clouds. Zeus was quite rightly enraged by this, and lashed Ixion to a wheel of fire, condemning him to spin around in Tartarus for the rest of eternity. For all the criticism Zeus and the other gods get, this is one time when he delivered Laser-Guided Karma and Kick the Son of a Bitch.
In older Catholic teaching and Word of Dante, the only truly unforgivable sin is to commit self-murder (suicide), since you're not alive anymore to be forgiven afterward. In recent years (since the Second Vatican Council), the Roman Catholic Church has ceased to teach that suicide is unforgivable. Quoting from the Catechism of the Catholic Church, sec. 2283: "We should not despair of the eternal salvation of persons who have taken their own lives."
The Catholic teaching on mortal sin is that it must be a deliberate act with the knowledge that it is a mortal sin. A completed suicide is unforgivable for someone who understood it to be a mortal sin and freely chose to commit it anyway. Not so for someone who is clinically insane and therefore lacking full control over his/her faculties. Some Christians hold that nobody who actually wants to die could be considered sane in any normal sense, so suicide is never actually a sin.
Further, this analysis assumes that the death is instantaneous. A mortally wounded person is still capable of a deathbed conversion, even if the mortal wound was self-inflicted. Confession and/or the Anointing of the Sick can be validly received to effect the forgiveness of mortal sins provided that the penitent has (at a minimum) sorrow for his/her sins arising out of fear of God's wrath.
The old rule of suicide being a mortal sin was an Obvious Rule Patch when some early Christians realised that, as Heaven is infinitely better to life on earth, there was no point hanging around here, and that the most logical course of action for a true believer was to commit suicide immediately after baptism, both to minimise their suffering and to avoid the risk of sinning.
In the book of Revelation, taking the "mark of the beast" and worshiping his image is considered a Moral Event Horizon.
According to various verses in the New Testament, rejecting the offer to accept Jesus as savior and rejecting His gift of forgiveness and salvation can be seen as a Moral Event Horizon. Note that this happens during the person's death.
According to Orthodox Christianity, there is no Moral Event Horizon as long as a man repents. However, by commiting sins (which we always do), he can go to the state of unrepentance. Only this counts. And a suicide, as mentioned before, DOES count as a Moral Event Horizon, as a man can only repent when he is alive. Even sin against the Holy Spirit is forgivable, as long as repentance follows.
Christian tradition holds that the Devil crossed it the moment he rebelled against God and literally brought evil into the world. Catholic theologians, such as Thomas Aquinas, have stated that, though a human may eventually repent and be forgiven no matter how grievous their sins, Satan and the other fallen angels will never do this, because it is not in their nature.
Orthodox Christianity states that the devil's (and later other demons) is the corruption of Adam and Eve (and later temptation, making the whole human race suffer the same Fate Worse than Death that awaits them. Taking You with Me in an extreme form. Before that, some saints state, redemption was still possible for them. After that...
Another condition that renders one unforgivable according to Christianity is not forgiving anyone and everyone, even if they did something seriously evil like murdering someone. The logic being that even the most minor sin against God is greater than anything humans can do to one another, so to expect God to clear our debts, we must be willing to clear ours. Though some Christians do take this to the extreme of not seeking justice for crimes done to them or their family, most Christians stress that this doesn't mean that offenders are not to be brought to justice for the offense, and it also does not mean having to interact with them or otherwise restore normal friendship/trust to them, or otherwise put oneself in danger of being hurt again.
In Islam, Shirk, translated as "idolatry" or "association" is stated as the only sin that God won't forgive on the Last Day. The concept is broad: it includes establishment of "partners" placed beside God or denying his existence. Saying that God has a son or is part of a Trinity as Christians do also counts as Shirk.
It's hard to pinpoint exactly when King Saul crossed it, but there are two candidates.
Until the second time David failed to show up after being invited to one of King Saul's banquets, Jonathan, who Saul was certain was first in line to succeed him, thought that King Saul was simply out of his mind. But when Jonathan gave him a cover story that David wanted to spend some time with his family, King Saul snapped, called him a son of a bitch, and – more heinous than that – actually tried to kill his own son.
If that doesn't sell you on the point that King Saul had sealed his own fate, his unrelenting destruction of a city of priests and the execution of most of the same, including their families – yes, women and children included – certainly will. How unnecessarily cruel was it? Only one of his men was willing to carry out the grisly mass murder.
Similarly, the sons of perditionnote Those who either, during their pre-mortal life, aligned themselves with Satan's plan of salvation, or, in mortal life, have "denied the Holy Ghost" i.e. rejecting and denying Christ after receiving a personal witness and a "perfect knowledge" of Jesus (see "blasphemy against the Holy Ghost" above) are not to benefit either of the celestial, terrestrial, or telestial glory, but instead are cast into the outer darkness with Satan and his angels.