My immediate reaction is the moveable type printing press. It changed the entire paradigm under which people lived by allowing people without access to information, new access. It changed the power structure and people's view of the world. It allowed knowledge of other new inventions, processes and ideas to be spread. Anything new is only useful if you know about it.

By this same token, I would lax if I didn't say that I think the internet is the printing press of modern times. It has again levelled the playing field in allowing easy access to information. People all over the world can see and hear and read about things they would not have known about before. It has again changed the power structure (small example: I can self publish with the use of the internet, publishing companies no longer are all powerful over what is out there to read) and again opened people's view of the world.

While we're stretching the definition of what an "invention" is, I'll throw out a process as a possibility. How about the development of processes allowing for the refinement of raw iron ore into steel, or the process of making glass out of silica sand? Without the ability to convert completely natural resources into processed materials, the mechanical items suggested above would not be possible.

I have to second the electric light bulb, which quickly transformed homes and cities into a new realm of modern convenience. It led to other uses for electricity, something that no one can do without today.

If you have ever lived through a summer in Texas, you will understand that the correct answer to this question in the Air Conditioner.  From a more serious perspective, I would say agriculture in general.  It allowed people to stop wondering around in search of food and led to the development of civilizations.

If you mean a machine, I'll agree with the moveable type printing press. But I'd actually argue that a number of medical advances, notably the smallpox inoculation or the use of penicillin may have changed more lives. Another possibility could be some agricultural invention, like the steel plow, or one of the techniques that led to the elimination of the fallow. Then again, one might also argue that these advances wouldn't have been impossible without the spread of information faciliated by the printing press.

It is the printing press.  Other things are, of course, immensely important, but the invention of the printing press made it possible for knowledge to be widely disseminated and stored.  This completely changed what is possible in our society.

The electric light bulb is a great invention, allowing people to work at night, to buld tunnels underground for subways and highways, and helping to grow plants indoors.

Many people will suggest the invention of certain medicines as "the greatest invention", like Penicilin and Aspirin.