He was born in 1921 in Blackford, Kentucky. His father did shoe repair and his mother was a drugstore clerk. Despite their own lack of education, his parents encouraged him to seek an education from an early age. He attended primary school in Hopkinsville, Kentucky and graduated from Hopkinsville High School in 1939. He served in the Army Air Forces as a cryptographer during World War II, and began reading about human psychology at that time.

He graduated from the University of Kentucky in 1948 and returned to receive a masters degree in psychology. He received his doctorate in psychology from Stanford University in 1951.

After receiving his PhD, he became a staff scientist at MIT's Lincoln Laboratory, doing military research. In 1953 he joined the Human Resources Research Office at Fort Knox, where he did human factors research relating to the Army.

He served on the faculty of Chico State College and Indiana University Southeast and as a staff psychologist for the Kentucky Department of Corrections. In 1969 he joined the faculty of his alma mater University of Kentucky in the psychology department. He spent four years as chairman of the psychology department. He spent the next 20 years of his career here, until retirement.

He served as president of the Kentucky Psychological Association and was a fellow of the American Psychological Association.

He was a critic of pseudoscience in the practice of psychiatry and psychotherapy, and of the coercive nature of psychiatry. He wrote a book on this topic and allied himself with Thomas Szasz in this criticism.

His parents instilled skepticism in him from an early age. He was interested in ghosts as a child, but was disappointed to discover upon investigation that the noises emanating from a nearby "haunted cave" were actually natural in origin.

As a university psychologist, he sometimes encountered cases with a paranormal element. He would do his best to find a non-paranormal explanation or resolution for these cases, and eventually gained a reputation as a "ghost buster".

When Joe Nickell was seeking an advanced degree at the University of Kentucky, the two met. They later worked together on several paranormal investigations and co-wrote a book on the topic. Nickell once said, "No one knew more about alien abductions than Robert Baker."

After retiring from the university in 1989, he devoted much of his time to scientific skepticism, writing several books on related topics including hypnosis, ghosts, alien abductions and false memory syndrome. He used his expertise in psychology to argue that many paranormal phenomena can be explained via human psychological effects such as hallucinations or sleep paralysis.

He was an organizer with and served as president of the Kentucky Association of Science Educators and Skeptics. He wrote numerous articles and book reviews for Skeptical Inquirer magazine and CSI's Skeptical Briefs newsletter.

In 1999, a panel of skeptics named him among the two dozen most outstanding skeptics of the 20th Century.