1. The number 'zero'. Mathematics and science could not have developed without it. (Many scientists, and nearly all mathematicians, regard the invention of a symbol to represent zero as the greatest invention of all time).
2. Radio. Much of the development of society, throughout the 20th of century, depended upon rapid communications. ('Radio' in this sense, embraces all forms of radio communication, including television and satellite technologies).
3. The transistor. (The electronic component, not a portable radio set!). The development of the transistor led to rapid advances in solid state electronics. Without it, we'd have no computers, no internet, no cash machines, no digital TV or radio, no CD or DVD players, no equipment for recording TV programmes, no modern aircraft, no digital cameras, no mobile phones, no answering machines, no MP3 players, . . . etc).
4. The symbolic representation of the square root of minus one. Without it, mathematical modelling would have been greatly hindered. Many developments in science, technology and engineering, which we take for granted, could not have happened.
5. The 'waiter's friend' corkscrew, for obvious reasons (hic!). OK, if you want me to stay serious, I'll replace that with the sewage treatment plant. Without proper sewage treatment, we'd all be up to our necks in the brown stuff ;-)
Further ideas here:
http://encarta.msn.com/column_10greatestinvent ions_tamimhome/The_10_Greatest_Inventions.html
Chris