I come from a primarily religious background, so I'm not sure my position will be helpful for a non-religious solution.
But I will go into how I think about these things anyway, because its an important question with important answers.
Basically, I consider death as a transition. This life's purpose isn't to perform to any human standard; so wealth, fame, notoriety, happiness, etc. are not direct goals of mine. Nor is it a goal of mine to have a lasting impact. I'm not here to impress anyone, or look or act in any particular way.
Some of those things may be a byproduct of how I live my life, but they are not necessary conditions to live 'successfully'.
I think that I should address my definition of success: 'success' in this life means to love God and love people. So what is 'love' (baby, don't hurt me)? Love is not an emotional state, rather it is the active process of listening, respecting, and acting on another's words and needs.
Coming back to mortality: being reminded that I am not long for this world reminds me of the greater purpose of life, relieves stress from performance related anxiety, and curbs worry about physical/mental illness and other maladies, money issues aren't issues anymore, and so on, because I know God will take care of me.
Think of the billions of years that passed by before you were born. Were they bad for you? Was there any pain? Do you worry about them, or even pay any attention to them?
Perhaps things will be identical to you after you've died, and therefore absolutely nothing to worry about.
As a non-believer, I believe that we have just this one life, so make the best of it and enjoy it without worrying.
Oh, and try to leave the place a bit better than when you arrived ;-)
