Thanks for the reminder. Here's my shot. Perhaps the most challengingly important inventions are those that open up new moral dilemmas, and thus make some people question whether the invention should have been allowed (or precursor discovery sought) in the first place. This even applies to Howard Gardner's suggestion of classical music: I would add Adorno's (I think) statement that, in contrast to some composers, it is impossible to find evil that could have been reinforced by any note written by Mozart. On the other hand, I believe Wagner is still banned in Israel.
But my own suggestion is closer to my professional interests. As delightfully examined in Jared Diamond's Guns, Germs and Steel, writing was at least one of the most important inventions of all time, but Sumerian cuneiform is too old for me to offer it, by 3000 years. So, in agreement with Philip Anderson's nudge, the printing press is my response to the question. After all, even the World Wide Web is just a printing press with electronic and photonic elaborations. But I can't resist looking forward at an editorial fantasy, ignoring all sober estimations of the difficulties involved: a cumulative invention which, if fulfilled, would certainly have a capacity for good and evil. To quote William Gibson's Neuromancer:
".. and still he dreamed of cyberspace...still he'd see the matrix in his sleep, bright lattices of logic unfolding across the colorless void..."
No keyboard, mouse or screen, just neural connections and a many-dimensional space of, at least, information, to explore, organise and communicate at will — perhaps, dare I presumptuously suggest, with occasional help from an editor. I fear it's too much for me to expect, but my grandchildren could love it.