Let's ignore discoveries (germs) and technique (scientific method) for starters before determining the greatest invention. I also think that the printing press, a device invented to rip-off the bible buying public, should be relegated to its rightful place as number two to a newer invention: computer networks. While it is quaint to romanticize the past by citing the printing press, steam engines or 18th century lug nuts, we ignore the fact that our inventiveness as a civilization is increasing not decreasing and newer inventions might be the most important inventions. And let's choose an invention in and of itself and not argue about derivatives. Right now the invention that is revolutionizing the world (more than TV, for sure) is the computer network — the Internet in particular. And, for what it's worth, arguing that none of this would be possible if man hadn't learned to grunt first, therefore grunting in the most important invention is nonsense.
More interesting in this artificial discussion is how most of the participants, including myself, have chosen an invention from their particular specialty. Perhaps we should ask the question: what is the most insidious invention of the past 2000 years? How about specialization? Look at how insidious it is in this discussion. So much so that it's frightening. Change the topic! Discussing the most insidious inventions would be more fun than talking about the importance of hay, the concept of infinity or Goedel! Just think of the possibilities. We can nominate plastic, the stock market, roller pens, the vibrating dildo, sitcoms, the literary agent, Microsoft Visual BASIC, the animated cartoon, CNN, the wrist watch, roller blades, the spinach souffle. The possibilities are endless. Let's start over.