Ideally: the continuation of our consciousness/mind in some form. I think it would be a complete waste for us to live our lives, and gather so many experiences and memories - positive and negative - only to lose them all, along with our personhood, by ceasing to exist; this is a very disturbing thought for me.
Realistically: I think that once biological death occurs we cease to exist completely, and there is no afterlife or new state of being, and no soul or anything else mystical or spiritual.