Since a number of people have already mentioned the printing press (which would also definitely be my own # 1 choice), let me put in a good (and somewhat whimsical) word here for the flush toilet. Supposedly the first of these was invented in the late 1590s by Sir John Harington for his godmother, Queen Elizabeth I of England. There seems no need to elaborate on the usefulness of this invention; simply try to imagine modern life (especially in a large city or skyscraper) without it. It's easy to take these kinds of inventions for granted, but I think we can all feel grateful to good old Sir John (no pun intended).
From the 14th to the 16th centuries, science and technology burgeoned, leading to technological advancements in architecture, painting and--as is much heralded--printing, to name the top few. Printing--well, we all know what it did--painting surged to new levels as linear perspective was developed and architecture put forth new appearance as new domes and fortification shapes--respective of the canon--emerged. Technology, of course, is the practical implementation of the discoveries of science.
I have to agree with #2 here. The printing press had a seismic impact on Renaissance society and resulted in so many other massive changes, such as the Reformation. The distribution of Luther's ideas and others like him had massive effects on society at the time. The free dispersal of ideas also played a key role in the development of European society.
What about Leonardo da Vinci? He was a prolific inventor of the Italian Renaissance. He designed a glider, helicopter, and a parachute; he created an automobile run by springs, and he invented a three-tier machine gun.
I am going to go out on a limb here and say that many of the technological andvances of this era were not even realized until much later. I am thinking of advances in health care and inventions that were thought up then by the likes of Leonardo da Vinci.
Another important technological advance during the Renaissance (although it is nothing compared to the printing press) is the development of astrophysics through the writings of Copernicus and Galileo. The heliocentric theory had dominated the theological and scientific thought for centuries before it was put to the test. As a result of the observations conducted in heavenly bodies, more adjustments and better changes came to objects such as the screwdriver and the telescope just to mention a small example. Yet, those little changes make up for a huge effect in civilization.
There were so many important technological advances in the Renaissance that it is hard to narrow this question down. I would argue that the most important of these advances was the printing press.
The printing press was so important because it made printed materials much cheaper and more widely available than they ever had been before. This allowed more people to become educated and it allowed ideas to spread rapidly. This facilitated such huge social changes as the Protestant Reformation. People across Europe were able to read religious arguments and think about them for themselves. This led to a fundamental change in society.
The printing press is, in my mind, the most important technological advance of the Renaissance.