In 2010: Odyssey Two, Arthur C. Clarke's first sequel to 2001: A Space Odyssey, HAL 9000 is described by Dr. Chandra as being caught in a "Hofstadter-Moebius loop".

Hofstadter's book Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought was the first book ever sold by Amazon.com.

When Martin Gardner retired from writing his "Mathematical Games" column for Scientific American magazine, Hofstadter succeeded him in 1981-1983 with a column entitled Metamagical Themas (an anagram of "Mathematical Games"). An idea he introduced in one of these columns was the concept of "Reviews of This Book", a book containing nothing but cross-referenced reviews of itself which has an online implementation. One of Hofstadter's columns in Scientific American concerned the damaging effects of sexist language, and two chapters of his book Metamagical Themas are devoted to that topic, one of which is a biting analogy-based satire entitled "A Person Paper on Purity in Language", in which the reader's presumed revulsion at racism and racist language is used as a lever to motivate an analogous revulsion to sexism and sexist language. Another column reported on the discoveries made by University of Michigan professor Robert Axelrod in his computer tournament pitting many iterated Prisoner's Dilemma strategies against each other, and a follow-up column discussed a similar tournament that Hofstadter and his graduate student Marek Lugowski organized. The "Metamagical Themas" columns ranged over many themes, and included, to name just three, one on patterns in Frederic Chopin's piano music (particularly the études), another on the concept of superrationality (choosing to cooperate when the other party/adversary is assumed to be equally intelligent as oneself), and one on the self-modifying game of Nomic, based on the way in which the legal system modifies itself, and developed by philosopher Peter Suber.

Hofstadter was married to Carol Ann Brush. They met in Bloomington, and married in Ann Arbor in 1985. They had two children, Danny and Monica, but Carol died in 1993 from the sudden onset of a brain tumor — glioblastoma multiforme — when their children were five and two. The Carol Ann Brush Hofstadter Memorial Scholarship for Bologna-bound IU students was established in 1996 in her name. Hofstadter's book Le Ton beau de Marot is dedicated to their two children and its dedication reads "To M. & D., living sparks of their Mommy's soul".

Both inside and outside his professional work, Hofstadter is driven by a pursuit of beauty. He seeks beautiful mathematical patterns, beautiful explanations, beautiful typefaces, beautiful sonic patterns in poetry, and so forth. Hofstadter has said of himself, "I'm someone who has one foot in the world of humanities and arts, and the other foot in the world of science." He has had several exhibitions of his artworks in various university art galleries. These shows have featured large collections of his gridfonts, his ambigrams (pieces of calligraphy created with two readings, either of which is usually obtained from the other by rotating or reflecting the ambigram, but sometimes simply by "oscillation", like the Necker Cube or the rabbit/duck figure of Joseph Jastrow), and his "Whirly Art" (music-inspired visual patterns realized using shapes based on various alphabets from India). (The term "ambigram" was invented by Hofstadter in 1984 and has since been taken up by many ambigrammists all over the world.)

Hofstadter has composed numerous pieces for piano, and a few for piano and voice. He created an audio CD with the title DRH/JJ, which includes all these compositions performed primarily by pianist Jane Jackson, but with a few performed by Brian Jones, Dafna Barenboim, Gitanjali Mathur and himself.

Hofstadter's writing is characterized by an intense interaction between form and content, as is exemplified by the 20 dialogues in GEB, many of which simultaneously talk about and imitate strict musical forms used by Bach, such as canons and fugues. Most of Hofstadter's books are characterized by some kind of structural alternation: in GEB between dialogues and chapters, in The Mind's I between selections and reflections, in Metamagical Themas between Chapters and Postscripts, and so forth. Both in his writing and in his teaching, Hofstadter stresses the concrete, constantly using examples and analogies, and avoids the abstract. Typical of the courses he teaches is his seminar "Group Theory and Galois Theory Visualized", in which abstract mathematical ideas are rendered as concretely as possible. He puts great effort into making ideas clear and visual, and asserts that when he teaches, if his students do not understand something, it is never their fault but always his own.

Hofstadter is passionate about languages. He has studied many of them, and speaks them to varying degrees. In addition to English, his mother tongue, he speaks French and Italian fluently (the language spoken at home with his children is Italian). At various times in his life, he has studied (in descending order of level of fluency reached) German, Russian, Spanish, Swedish, Mandarin, Dutch, Polish, and Hindi.[citation needed] His love of sounds pushes him to strive to minimize, and ideally get rid of, any foreign accent.

Le Ton beau de Marot: In Praise of the Music of Language is a long book devoted to language and translation, especially poetry translation, and one of its leitmotifs is a set of some 88 translations of "Ma Mignonne", a highly constrained poem by sixteenth-century French poet Clément Marot. In this book, Hofstadter jokingly describes himself as "pilingual" (meaning that the sum total of the varying degrees of mastery of all the languages that he's studied comes to 3.14159...), as well as an "oligoglot" (someone who speaks "a few" languages).