While Buddhists believe in reincarnation, this is not simply a happy solution to the problem of death.
At death, we will reap what we sow, as we do in life. This means that, after a period in an in-between state (a Bardo), actions taken to hurt others through ignorance will result in a future life where we are mistreated. Actions taken to help others will result in us being treated well by the world and by others.
Buddhists often believe that there is no magic line separating humans from animals. Every creature is connected through the cycles of life, and dependent upon each other. As there is no distinction between the different species, when a person dies they are as likely to be born as an animal as another person. And indeed, a person is more likely to be reborn as an animal or insect, as there are many more animals in the world than human beings.
For this reason, a human life is considered a very precious and rare opportunity. It should not be wasted. Death is something to be constantly reminded of and ready for.
A belief in reincarnation is called reincarnationism. for more information, the International Society for Reincarnation Studies (ISRS) have a website at Reincarnationism.com. There you can read more information and watch clips of people who remember some of their past lives. The ISRS is a non sectarian group that represents Buddhists, Christians, Atheists, Jews and many other belief systems.
A book outlining reincarnation and the amazing story of Tibetan masters that have chosen to be reborn in America, Canada, and elsewhere in the West is called Reborn in the West. You can also read about the unknown history of reincarnation in Christianity in Jesus and Reincarnation.
The best guide written about the death process, and how best to prepare for it is The Tibetan book of Living and Dying, by Sogyal Rimpoche.
Read Related Beliefs:
Life is Precious
You Will Reap What You Sow