In later, more localized adaptations of Buddhism, there are many hells 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."
Avici hell literally 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 only reserves Avici for complete monsters only.
Also, considering the cyclic nature of Buddhist cosmology, even sins fit for Avici is 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 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 unforgiveable 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.
In the book of Revelation, taking the "mark of the beast" and worshiping his image is considered a Moral Event Horizon.
Judaism has one sin which can only be atoned for through death - "desecration of the Divine Name", which basically means hurting God's reputation. One interpretation is that it is considered so heinous because it can cause others to turn away from God and to sin.
For many former Christians there are many things that God does throughout the book that can be considered the Moral Event Horizon, from advocating rape, slavery, condemning an entire species to a short, pain-filled life for being influenced by a creature he himself made. Put it simply, even without logic, the pure evils that can be read in the bible can cause people to turn against their faiths permanently.