Just in case there are any misconceptions about this, most serious atheists don't believe in reincarnation or spirits any more than we believe in hell. What defines "you" is what you think and feel, and how you interact with the universe. When this stops happening, you're not you anymore. So you simply stop existing.
If this idea scares you, think about all the millions of years that passed before you were born. Do you remember it? Was that scary? Interestingly enough, the fate that Christians find so inconceivable -- complete nonexistence -- is regarded by Buddhists as the best possible outcome for your life ("Nirvana").
Some people take this a step further and argue this way: "The first law of thermodynamics says that matter and energy cannot be created or destroyed. Since life is a form of energy, it must go somewhere." We don't see life as a self-contained form of energy. It's more of a process that matter and energy goes through.
Some people find this idea disturbing. They really want to be around forever. We all would. But realizing that you won't be around forever makes this life seem more valuable in a way. Since you only get one shot, it's important to do the best you can to be happy and make others happy before you're done.
Posted in: About atheism