I can think of no substantial evidence to support the ancient assertion of an afterlife, however much I want to believe that after I die, some thinking, feeling part of me will continue. The thinking, feeling part of us humans falls apart in such a complete way that it is difficult to believe that, even if the conscious component of the human experience were to continue, it would continue to identify itself as human.
However, there is some tepid evidence for paranormal activity that should be considered. While truly scientific evidence for such occurences are rare, they do exist. I think there may be some mechanism which accounts for such circumstances (evolved capacity to quantumly entangle brain patterns, perhaps even with outer materials or other people?) but we must, of course, further research the problem.
Since we do not understand why humans experience consciousness, I don't think that anyone is qualified to talk about exactly what happens after you die. Surely, you wouldn't be 'you' anymore, and in all likelyhood not at all human, but I'm inclined to believe that the phenomenon of conscious experience is not unique to humans, or unique to animals, or even unique to life. As it is yet unexplained, the simplest explaination is that it is simply an integral part of the whole universe.