Beer
A lot of college kids have put this one forth, and I have to say it's not without merit. It is believed that grain was first harvested and domesticated for the purpose of alchohol. Therefore, our entire civilization never would have been created if not for the discovery of the fermenting process. Without beer as it were, you could argue we would still be hunters and gatherers living by our wits alone. I'd be dead.
Music
One and the same with math, music is the universal language. While it's origins may be forever unknown, we do know that people's natural instinct is to move to music. Babies enjoy it and so do we, even if we have our own particular tastes. As laughter and a smile are the natural responses to happiness, so is music a natural response to living... so perhaps it's not much of an invention at all, it always was there we just put a name to it.
The Complex Plow
You can thank this handy do-dad for the end of the dark ages. With its creation Europeans were able to till soil that they were unable to use before hand. Thus much shallow soil was able to be used for farming. It was also a more effecient tool for plowing the soil already used, and thus there was more food and less work. More food allows for larger populations, less work allows for other pursuits. One could argue the renaissance could not have been possible without this invention.
The Printing Press
This was the renaissance. Invented around the fourteenth century this invention made the largest transfer of information out of the elite's hands and into the general population possible. Only a handful could read and write, and only the clergy and the noblemen could afford their services. Many noblemen were illiterate, and hired others to write for them. The printing press allowed not just anyone to read but write as well. The only best seller around was the Bible, but with this invention ideas could be spread over vast distances like wild fire. Thus a movement towards intelligance was founded which we feel to this day.
The Steam Engine
Allowing for the industrial revolution, the steam engine put coal on the map. With these babies people created industry, allowing for mass production and uniformity of goods to be a reality. If this was a good thing is not my place to say, all I can say is it was important in shaping the world we have today, even if some may not like it.
The Computer
While it was invented earlier than half way through the twentieth century, it did not come into its own till much later, after it shed its vacuum tubes and punch cards. The computer has had great influence over our lives. It has shrunken the distance between places on the world to the edge of tangability. It has taken over our lives, running our jobs for us. It has allowed for vast warehouses of information to be stored in a single computer while allowing anyone's thoughts to deseminate to the rest of the world. The computer has allowed everyone to become connected, yet it also drives us apart. Certainly it is an invention worthy or summation.
Grand Unified Theory
While not technically an invention, or necessarily existant, if Grand Unified Theory was discovered surely it would be the greatest accomplishment of mankind... ever. It would allow unlimited energy, an end to waste, and control over the very universe itself for starters. It could lead to so much power, one has to wonder if mankind will ever be ready for it.
personally, I would like to think that the greatest invention is sex. It has a purpose, the continued existance of our species; it's practical, most everyone can do it, everyone can have it done to them; and it's fun, name me one woman that doesn't enjoy sex and I'll put a smile on her face. don't believe me? give me a recent picture and her number and we'll see who laughs last. Let's face it, these days its cheaper than going out to the movies.