Life your life positively and dont think about rebirth, is the only way to pop out of the cycle of rebirth.
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Eternallyephemeral: I don't think the above answer is answering the question, which is vague itself. If you're talking about the cycle of rebirth in Hinduism (and Buddhism), the escape is called samsara, and escaping the cycle, the body is shed by the soul for a final time.
Moksha
Escape the cycle of death and rebirth.
Buddha developed the teachings and process of allowing humans to escape suffering and the cycle of death and rebirth that were later called Buddhism.
Nirvana is not holiday, celebration or card giving occassion. It is the state of unselfness unity that can be achieved by an enlightened being after death and the escape from the cycle of death and rebirth.
all earthly ties - they are what trap us in the cycle of rebirth through the 3 root poisons of greed, hatred and ignorance - only once we have escaped these poisons can we be free from rebirth and so escape all suffering - ultimately leading to enlightenment
By following the paths of Lord Chaitanya, Buddha, Moses, Christ, Mohammad. Each carried the message from The Creator in a form that was acceptable to the consciousness of the peoples the message was intended for.
The cycle of rebirth is referred to as samsara like the constant ebb and flow of the oceanic tide. ^ the answer above is too vague. Samsara is the cycle of life, death, and rebirth/reincarnation, and it is a Hindu concept as well as a Buddhist concept. Hindus and Buddhists believe that the soul wears the physical body like an article of clothing, and that there is no such thing as death. When the physical body "dies," the spirit leaves and moves onto the next physical body, reborn, dies, is reborn, and so on. It is an endless cycle, and the only way to escape the cycle (mokhsha) is to achieve nirvana (according to Buddhist philosophy), which is the absence of suffering. To do so, one must purge oneself of desires, for desires are what spawn suffering, and when one achieves this, the cycle is broken.
Reincarnation
http://www.google.com/url?sa=t&source=web&ct=res&cd=4&url=http%3A%2F%2Fwww.xanga.com%2Frrandi99%2F635775036%2Fhinduism-atman-is-brahman-as-brahma-is-atman.html&ei=MQZKSf_0KozQMdWF7LYP&usg=AFQjCNGA7uZU-m_fLk1xk9ihR-8e1A-R-A&sig2=XqtcRo70oeLZjbtKTAJsBA
The cycle of rebirth carries on indefinately until enlightenment.
Decline or rebirth stage
Moksha, which means emancipation or release, is freedom from Samsara in Hindu, the cycle of death and rebirth. One who achieves Moksha is one who has achieved total self realization and self knowledge. Moksha, along with Dharma, Artha and Kama, represents the four goals of human life.