It's not a contest. But Star Trek inspired the invention of the cell phone and the tablet, and put a lot of real scientists, engineers and astronauts on their career track from an early age. Who knows, really, the extent of invention that can draw its germination back to Trek in some way? Not even mentioning the real social ramifications of exploring - not space, but an inclusive, optimistic, illuminated future.
Dr Who? Please. Where's our sonic screwdriver. Star Wars? Please. Toy bantha poop and hot laser death from above. Harry Potter? Giving kids all over the world - a stick.
Who's the big daddy?
Trek inspired Bill Gates, Steves Jobs & Woz, Linus Torvalds and all their pocket-protector-armed minions. Trek gave everyone a hand in creating better-reasoned societies. Even the first Space Shuttle was named after Trek's USS Enterprise.
They all owe the existence of Information Age fandom to Trek. Heck, it could even be argued no Trek, no Information Age as we know it.
But all of that is not Star Trek. Star Trek is just the most relevent-to-date fictional manifestation of...all of that genius at play.
It's not a contest. But to invoke cultural relevance, let alone fandom, without respect to Star Trek is base ignorance of one's own origins - in whatever vehicle that cruises the global, cultural superhighway carved out of the dark wild by Star Trek - and its fans.