Well, as an atheist I do not believe in life after death - although I thought Fljotsdale's answer about living on in the sense that our life impacts on others and the ecosystems that will be nourished by our remains was an excellent point, very well made.
I don't believe in souls, just that we are biological organisms (albeit very complex ones) and therefore death is a process whereby once your braincells and nervous system have suffered from prolonged lack of oxygen you are 'braindead' and that is final, and is followed by the disintegration and digestion of your body tissues by enzymes and bacteria (amongst other things).
Sorry, that is probably not a very cheery thought. However as far as I am concerned it is the only rational explanation.
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Time is an illusion. Lunchtime doubly so.
Epona of The Laughing Hyenas
Proud winner of the 'Most Useless Post 250 Has Ever Seen' Award 2001. "I'd just like to thank my friends and family, without whom none of this would have been possible..."