I think a better question for me personally would be: "what dreams have I purposefully turned away from?" And better yet, 'why?'
I grew up with people telling me how smart I was, and how I was going to do great things, and 'oh, I expect to see your name in a newspaper someday', etc. So I dreamt big. Spaceships, mining the stratosphere of Jupiter or the asteroid belt, and so on. Kid dreams without restriction.
I began stepping back from these very big things when I got married. What kind of time commitment will it take for me to be the absolute best? What would it mean for me to dump my heart and soul into something other than the one I love? At the end, when I've got ten minutes of life left, would I be satisfied with what I had done?
I don't like the answers I have to the questions above. The bottom line for me is the question "What really matters? Not just to me, but when considering the largest scope of reality."
The value of human life is not our achievements, or our legacy that we leave behind, or a name that will be remembered. Rather, our value is our capacity to love God and love other people. In fact, we aren't asked to do anything more than that.
Sure, we are given passion and desire to do and to build and to create. And we should follow that to the extent we are able (beyond our own frail fears and mental limitations). But the end of the line isn't what we achieve. It can't be. Because (depending on who you listen to) in a few trillion years it'll all wind down into a steady-state soup. Meaning will be lost to the dead and dying universe.
TL;DR: leave it a dream if you have some end-goal as the reason for the doing of the thing (ie, money, fame, wealth, notoriety, etc.). It's ok to have some end goals, just don't make them the reason you do something.