Transcription of a right-handed double-helical DNA requires a relative rotation of the RNA polymerase and its nascent RNA around the DNA. We describe conditions under which the resistance to the rotational motion of the transcription ensemble around the DNA can be large. In such cases, the advancing polymerase generates positive supercoils in the DNA template ahead of it and negative supercoils behind it. Mutual annihilation of the positively and negatively supercoiled regions may be prevented by anchoring points on the DNA to a large structure, or, in the case of an unanchored plasmid, by the presence of two oppositely oriented transcription units. In prokaryotes, DNA topoisomerase I preferentially removes negative supercoils and DNA gyrase (topoisomerase II) removes positive ones. Our model thus provides an explanation for the experimentally observed high degree of negative or positive supercoiling of intracellular pBR322 DNA when DNA topoisomerase I or gyrase is respectively inhibited. We discuss the implications of our model in terms of supercoiling regulation, DNA conformational transitions, and gene regulation in both prokaryotes and eukaryotes.