Recommendations for popular books on Gödel's incompleteness theorems include "Incompleteness: The Proof and Paradox of Kurt Gödel" by Rebecca Goldstein, which explores the implications of Gödel's work. "Gödel: A Life of Logic" by John L. Casti and Werner DePauli is another suggested read, providing insights into Gödel's life and contributions to logic. Additionally, "Gödel's Proof" by Nagel and Newman is noted for being accessible without requiring a technical background, making it suitable for a general audience interested in the subject.