The Sumerians made the first ancient civilization. They lived in Mesopotamia in the area known as the "Fertile Crescent" which exists between the Tigris and Euphrates rivers.
One of the things that they are best known for is that they were the first literate society. At first, they communicated via simple pictures, but by 2000 BC, they had developed a completely phonetic language. (Editor's note, 12 November 2002: read "writing system" instead of "language" in that sentence. All spoken languages are phonetic. -fab)
The Sumerians were also the first culture to use widespread irrigation techniques. Since they lived in what is now Iraq, rain was scarce, and they had to invent other methods of sustaining their agriculture.
Their religion was polytheistic and centered around many gods who had human qualities. In fact, according to their creation myth, the lower class of gods was stuck doing the drudge work. The gods became lazy, and created humans out of clay to do the work for them. This myth also explains the importance of clay to their society. They used clay to make pottery, tablets for writing, as well as bricks for their houses.
Socially, they had a hierarchy similar to that of the caste system in India. The highest-ranking citizens were the priests who were believed to be in direct communication with the gods.
Their impact is still felt today, as they invented the wheel, astrology, and they had a very advanced mathematical system. They wrote lots of poetry and literature which has been preserved on clay tablets. Even after the Babylonians conquered them, their culture was adopted by the Babylonians.