Cohen graduated from the University at Albany, SUNY in 1971, with a Bachelor of Arts in music. He spent several years "writing humor pieces, essays, and stories for leading newspapers and magazines"; his first paid, published piece was in 1976 for The Village Voice In 1981, his book of satiric letters, Modest Proposals, was published by St. Martins Press.

Cohen was a writer on Late Night with David Letterman for 950 episodes over seven years, starting in 1984. He shared in three Primetime Emmy Awards for Outstanding Writing for his work on the show.

Cohen wrote for TV Nation, sharing in a Primetime Emmy Award for Outstanding Informational Series in 1995. In 1996, he became the original head writer for The Rosie O'Donnell Show.

Cohen wrote for Slate starting in 1996. At Slate, he became known for "News Quiz," a satiric reader-participation feature which began in February 1998 and ended in November 2000. He also co-wrote a first-season episode of Ed, first broadcast on February 14, 2001.

From 2001 to 2005, Cohen also answered listeners' questions on ethics for the National Public Radio radio news program, All Things Considered.

A play by Cohen about the eighteenth century boxing champion Daniel Mendoza, “The Punishing Blow,” debuted in 2009, at the Woodstock Fringe Festival.

In a public speech archived as a podcast on the New York Times podcast website, Cohen outlines his personal beliefs about ethics as being ultimately dependent on a person's immediate circumstances, while dismissing the notion that personal moral character might influence an individual's ethics.

Cohen categorically rejects the idea that individual people are inherently good or bad, asserting that in his opinion all individuals have in them the capacity to do good or bad at different times, in different contexts. In Cohen's view of ethics, individuals are all more or less the same with respect to ethics, but society is often to blame for the very existence of an ethical dilemma, which aligns him (by his own admission) with many of the beliefs of the Society for Ethical Culture; a fundamental premise of this ethical framework is that humans are morally obligated to promote changes in society so all people can lead more ethical lives.

Cohen was born in Charleston, South Carolina and raised in Reading, Pennsylvania, in what he has called a "suburban reform Jewish household."

He was formerly married to the writer and activist Katha Pollitt, with whom he has a daughter, Sophie Pollitt-Cohen.

Cohen donated $585 to MoveOn.org's voter registration effort in 2004, apparently in violation of Times policy, which had banned political donations in 2003. The Spokane, Wash., Spokesman-Review decided on June 20, 2007, to drop Cohen's column, which had been scheduled to begin running in the paper on the following Saturday, because of his donation. Cohen responded that he saw no ethical violation, because he viewed MoveOn as no more activist than other organizations, such as the Boy Scouts of America. Nonetheless, he said he would not make such donations in the future.