But "now" or even time itself doesn't exist as such -- it's a continuum. i.e. there's nothing special about "now", this moment in time, above any other moment in time. Even the direction of time is an illusion of sorts, because you only remember the past rather than the future due to a property of entropy (that bit's complicated).

Continuity of self is an illusion, caused by the storage of memory in your brain. If some super-advanced alien were to create an exact copy of you while you were asleep, then destroyed the original, the copy would wake up the next day and would truly be you as much as you ever were from one day to the next, anyway.

One way to look at it is to imagine your conciousness as existing only for each separate instant in time, but instantly creating its own past from stored memory, thus creating the illusion of progression through time. As far as the continuity of "self" is concerned, the laws of physics say that you might as well worry about where you were before you were born than after your death.

Why do you seem to be your current age rather than five years old, say? Because five-years-old-you is effectively a different person, as future-you is a different person, even as I, Swipecat, am a different person. As I've said, it's just storage of memory that gives your conciousness the illusion of connection to your past self.

There ya go. Study advanced science, and you'll know these truths for certain, because nothing else can possibly fit the observations. So you can either get existential angst about it, or just don't worry about it and enjoy life because continuity of self is a convincing illusion. Have fun.

Edit: typos.