Very interesting question, and as usual I'm incapable of offering a simple answer.
I think fire has to be disqualified from consideration. It's not something humans invented, nature sets fire to things quite regularly with no help from us. What humans did was invent various ways to make it and control it, but it existed without us. An invention I think has to be something that wouldn't exist without us, so if you want to put fire on the list it has to be one of the technologies we use to create and control it, not fire itself. I'd also be inclined to restrict it to a single invention, not a product like a helicopter or a computer that's the result of multiple inventions over many years.
Frankly I doubt it's possible to make a compelling case for any single invention that everybody would agree is the greatest invention ever, unless you can convincingly argue that homo sapiens wouldn't have survived without it, or at a minimum that the lives of a majority of humans would have been nasty, coarse, brutish, and short, without it. Alternatively, we could argue that the greatest invention ever is the one that's made the greatest difference in the lives of the largest number of people, and I think that one's dead easy: it's the method of analysis and testing of ideas we call science. My grandparents' generation, for instance, was the first generation in human history that could routinely count on most of its children surviving to adulthood and most of its females surviving into old age instead of being taken out early by the stress of multiple childbirths, childbed fever, plain old wearing out, stuff like that. Birth control, infectious disease control, waste management, clean water... It all comes from the scientific understanding of the world around us.
Other candidates for the greatest invention ever:
cooking: it greatly increases the list of what's edible, and is an important factor in disease control
the basic caveman-type toolkit: knives, bows, arrows, spears, clubs, all the things that enabled our ancestors to bring down bigger game and protect themselves from predators.
language: it's a bit problematic whether this is a human invention or an inevitable consequence of evolution, but we are a social species and our sociability and progress are much enhanced by our being able to talk to each other and pass our knowledge along to the next generation, in great detail.
writing: this is the repository of the most successful human cultures, the way we preserve and pass on the thoughts of the best minds among us.
Any others you can think of? I've had a long and busy day, and I'm getting tired and running out of ideas. Maybe we could try for a top ten list instead of a single invention?