Star Trek definitely shaped my education quite a bit. A few examples:
After reading The Physics of Star Trek I moved on to A Brief History of Time and became the only 13 year old at my school to have a conceptual understanding of what a "black hole" really was. From there I became interested in Brian Greene and I continue to read "pop astrophysics" to this day.
I also learned quickly that Star Trek character names and episode titles were often based on literary and/or historical figures. That lead to some really interesting times with the old Encarta and there have been many times that I've been able to follow conversations about Shakespeare, Greek myths, etc. solely b/c of my knowledge of some TOS episode.
In college I found myself drawn to humanist philosophy and also had an immediate appreciation for anthropology and it's ideas of cultural relativism. Probably not a coincidence...
Last month I started a talk at a professional conference by deadpanning a quote from "Leonard H. McCoy, MD - 1967." Most of the audience paid little attention, but a few smirked knowingly. Somewhat surprisingly nobody said anything.