I would also go along with the Buddhist-leaning/existentialist response -- In order to answer the question, there needs to be a precise definition of what it means to be 'me','I','you'(insert pronoun.) Sentient beings tend to identify themselves as discreet and static objects that retain a definite identity. We also tend to think of ourselves as something that exists outside of the environment in which we are immersed.
When you look closely, however, there is nothing about any one of 'us' that does not undergo change. Our thoughts, memories, and sensations are in constant flux. It is only our memory that allows us to retain any sense of continuity and discreet identity. The physical state of every unit within the body is also constantly undergoing change. The only thing that does not change is conscious awareness in the moment.
Are there other manifestations of conscious existence? Who knows. Is there something static and immutable about 'me' that exists and will continue to exist for eternity once 'my' conscious awareness has been extinguished? Do 'I' have a soul that carries around this identity by recording all of my stored memories so they can be used at a later time in a different environment?
Anyone who answers this question and is honest with themselves will likely realize that their emotions tell them yes while their intellect shouts back with a resounding no. In the end, it all boils down to whether or not you trust your emotions more than your reason.
As there is no empirical evidence for a soul or a personal existence after consciousness has expired, it certainly takes a leap of faith and an appeal to emotions to cling to these views. That doesn't make it wrong to answer yes; I cannot disprove such things. 'I' simply find it very hard to believe.
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