Christianity, being a very diverse religion that has many different interpretations, has a vast variety of different ideas regarding Heaven, Hell, and Purgatory. Heaven is generally a constant idea in Christianity: Heaven is the abode of God, in which either pleasure is given or suffering is lifted from the soul. Traditionally, Heaven is a literal place within nature that souls reside in after death; metaphorically, Heaven is the sense of closeness towards God after death.
Heaven is described in the Qur'an with amazing detail; this is a simplified version given: “The example of Paradise, which the righteous have been promised, is [that] beneath it rivers flow. Its fruit is lasting, and its shade. That is the consequence for the righteous, and the consequence for the disbelievers is the Fire.” (Qur'an, Ar-Ra'd, 35)
A very detailed explanation of Heaven is provided in Al-Wāqi`ah: “In the Garden of Pleasure, a [large] company of the former peoples and a few of the later peoples, on thrones woven [with ornament], reclining on them, facing each other. There will circulate among them young boys made eternal with vessels, pitchers and a cup [of wine] from a flowing spring - no headache will they have therefrom, nor will they be intoxicated - and fruit of what they select and the meat of fowl, from whatever they desire. And [from them are] fair women with large, [beautiful] eyes, the likenesses of pearls well-protected, as reward for what they used to do. They will not hear therein ill speech or commission of sin - only a saying: 'Peace, peace.' The companions of the right - what are the companions of the right? [They will be] among lote trees with thorns removed and [banana] trees layered [with fruit] and shade extended and water poured out and fruit, abundant [and varied], neither limited [to season] nor forbidden, and [upon] beds raised high. Indeed, we have produced the women of Paradise in a [new] creation and made them virgins, devoted [to their husbands] and of equal age, for the companions of the right [who are] a company of the former peoples.” (Qur'an, Al-Wāqi`ah, 12-40)
Hell is just as well described in the Qur'an. “And the companions of the left - what are the companions of the left? [They will be] in scorching fire and scalding water and a shade of black smoke, neither cool nor beneficial. Indeed they were, before that, indulging in affluence, and they used to persist in the great violation, and they used to say, 'When we die and become dust and bones, are we indeed to be resurrected? And our forefathers [as well]?' Say, [O Muhammad], 'Indeed, the former and the later peoples are to be gathered together for the appointment of a known Day.' Then indeed you, O those astray [who are] deniers, will be eating from trees of zaqqum and filling with it your bellies and drinking on top of it from scalding water and will drink as the drinking of thirsty camels. That is their accommodation on the Day of Recompense.” (Qur'an, Al-Wāqi`ah, 41-56)
In conclusion, Islam's ideas on Hell and Heaven are similar to the traditional literal interpretation of Heaven held by most Christians.
“‘If you live by my regulations, observe my mitzvot and obey them; then I will provide the rain you need in its season, the land will yield its produce, and the trees in the field will yield their fruit. Your threshing time will extend until the grape harvest, and your grape harvesting will extend until the time for sowing seed. You will eat as much food as you want and live securely in your land. I will give shalom in the land — you will lie down to sleep unafraid of anyone. I will rid the land of wild animals. The sword will not go through your land. You will pursue your enemies, and they will fall before your sword. Five of you will chase a hundred, and a hundred of you will chase ten thousand — your enemies will fall before your sword. “‘I will turn toward you, make you productive, increase your numbers and uphold my covenant with you. . . .”
“So if you listen carefully to my mitzvot which I am giving you today, to love Adonai your God and serve him with all your heart and all your being; then, [says Adonai,] ‘I will give your land its rain at the right seasons, including the early fall rains and the late spring rains; so that you can gather in your wheat, new wine and olive oil; and I will give your fields grass for your livestock; with the result that you will eat and be satisfied.’
Both of these verses show a very important concept in Judaism that separates it from Christianity and Islam: Jews believe in immediate and empirical rewards for good action and for following orders, as opposed to specific afterlife. (Source, Olam Ha-Ba: The World to Come) However, this is not to say that an afterlife is not mentioned. Olam Ha-Ba is a higher spiritual state of existence. It is described as a banquet hall or “home” away from the hotel of the world.
Sikhs believe in reincarnation. The Sri Guru Granth Sahib makes this quite clear. "Those who meditate on God attain salvation. For them, the cycle of birth and death is eliminated." (Guru Granth Sahib Ji, 11) However, a Heaven and Hell do exist to the Sikh. Sikhs believe that, before rebirth, souls are placed either in Heaven or Hell to be rewarded or punished for a temporary amount of time due to their actions on earth, then they are reborn - this cycle repeats until they break the cycle by obtaining oneness with God (Mukti, or Moksha), a goal similar to that of Hinduism.
You might find this little tidbit of information fascinating. Or not. This is the response realsikhism.com has to the idea of a permanant heaven or hell:
How do we know we are reborn? We take birth and we do die. Sikhism does believe in the existence of heaven and hell, however, heaven and hell are created to reward and punish, one will then take birth again until one merges in God. According to some religion, the soul either goes to heaven or hell after death and stays there. So, how are people and other animals being born on this Earth? Is God creating new souls? If He is then no matter how big is heaven or hell it is going to be filled. If you consider a lake as heaven and think of drops of water being added to it as souls, then no matter how big the lake is, if no drops of water is leaving the lake, it is going to be filled some time in future. Our souls just ending in heaven or hell after death and God creating new soul doesn’t make sense. If God creates new souls, then why are children born with disabilities? Souls are born with disabilities because of the bad deeds they committed in their previous life. It is up to God if he sends the soul to hell to make it realize the consequences of its actions or be born and make it realize in its next life.
Buddhism teaches the idea of reincarnation, without the transmigration of the soul. (Sources, What Reincarnation is Not) A person is “reborn” in a sense, but their soul has died in their previous body. As such, Buddhists hold to the anatta doctrine; this is their most radical difference with Hindus. Reincarnation is based on the karma of past lives.
Karma is a Sanskrit word from the root "Kri" to do or to make and simply means "action." It operates in the universe as the continuous chain reaction of cause and effect. It is not only confined to causation in the physical sense but also it has moral implications. "A good cause, a good effect; a bad cause a bad effect" is a common saying. In this sense karma is a moral law.
Nirvana is the ultimate goal in Buddhism: it signifies the end of the cycle of reincarnation and is regarded as salvation. Nirvana is the state of full enlightenment; as such, those who obtain this status are given the title of Buddha. Siddhartha Gautama is commonly considered the first Buddha by all Buddhist sects. One obtains this by following the Four Noble Truths, , and the Four Immeasurables, and the Middle Path. Along with this, Buddhists are expected to follow specific levels of sila: Five, Eight, or Ten Precepts.