Sumerians- They were one of the fist civilizations. They created cuneiform writing. The clay tablets give a very detailed look into the lives of the ancient people.
Akadians- They built on the Sumerian empire. They established the same language in much of the middle east.
Babylonians. Babylon was the largest city in the world for a very long time. It may have been eventually surpassed by Nineveh. They invented the zodiac which is still used by astronomers to map the sky.
Assyrians. They conquered much of the middle east and occupied Israel.
Hittites. They were famous for their chariots. The Egyptians and others copied them.