Where does the term "fun fact" originate?-- namely, not with the compositional meaning but rather with the idiomatic usage to introduce some sort of unusual, esoteric, absurd or otherwise "controversial" fact?
'Fun' and 'fact': the early years together
As JEL's answer details, the pairing of fun and fact as coequal elements in serial lists goes back many decades. In addition to JEL's 1853 example of "Fun, Fact and Fancy," searches of the Library of Congress and Elephind newspaper databases turn up multiple matches for a regular column titled "Fun, Fact & Fancy" in the [Clearfield, Pennsylvania] Raftsman's Journal (for example, in the issue of June 25, 1857), a regular column titled "Fun, Facts and Facetiæ" in the [Towanda, Pennsylvania] Bradford Reporter (for example, in the issue of October 26, 1865) and—somewhat later—a regular column in the "Children's Tribune" section of the New York Tribune called "Fun, Facts and Fancy" (for example, in the issue of July 20, 1919).
Significantly earlier than the 1853 Southern Standard example of "Fun, Fact and Fancy" is one from the New York Herald (May 5, 1849) that flips the order of fun and facts:
TRUTH WILL CONQUER.—FACTS, FUN AND FANCY, of the richest kind, will be found in the Scorpion of to-day. It contains the commencement of a brilliant German Romance; Dumb Love; more of the Romance of Passion, Wild Oats, or Amours of a Quaker; Mysteries of New York; Libertinism in Troy; Crim Cons at Albany and Washington; and the most spicy correspondence from Boston and elsewhere, of all the naughty doing, etc.; ...
And earlier than that is the headline "Facts, Fun, Fancies" in the Cadiz [Ohio] Sentinel (May 28, 1845).
Other early list matches that owe a debt to consonance include "Fun and Folly, Fact and Fiction" in the Evansville [Indiana] Daily Journal (August 22, 1850), "Of Fun, Fact, and Fiction" in the New York Daily Tribune (March 14, 1856), "fact, fun and frolic" in the [Washington, D.C.] Evening Star (April 21, 1862), and "Fun, Fact and Fashion!" in the Lansing [Michigan] State Republican (April 13, 1864),
An advertisement for a campaign paper in the [Warren, Ohio] Western Reserve Chronicle (May 21, 1856) breaks with the alliterative theme by offering a list that includes "facts, fun, and pepper." Likewise, an advertisement posted weekly in the [Oregon, Missouri] Holt County Sentinel (and later in other newspapers) beginning on July 7, 1865, promises "fun, fact and incident" in a magazine seeking subscribers. Yet another instance, appearing in an anecdote from the New Orleans [Louisiana] Daily Crescent (September 20, 1854), refers to "fun, fact and interest."
But even though these many examples establish a close proximity between fun and fact by the 1860s—especially as members of the the trio "fun, fact and fancy"—all of the instances I found involve fun and fact appearing as coequal list items, not as a words forming single term.
'Fun fact' as a single (and popular) idea
An gram chart of "fun fact" (blue line) and "fun facts" (red line) for the period 1900–2005 shows no sustained enthusiasm for either term until the 1970s, followed by a considerable ascent starting in the mid-1980s:
What happened to trigger that ascent? The likeliest culprit, I think, is an advertising feature called "Fun Facts" or "Fun Facts to Know & Tell," which ran for two or three years during the early 1970s in the color comics section of Sunday newspapers throughout the United States. Although the feature was sponsored (by Wrigley's Chewing Gum), it was drawn similarly to "Ripley's Believe It or Not" and "Cappy Dick," both of which presented bits of fresh trivia and amazing factoids in comic strip format every week.
Here is a brief mention of "Fun Facts" in Rick Marschall, "Cartoons and the Selling of America," in Marschall & Bernard, Drawing Power: A Compendium of Cartoon Advertising (2011):
When I was Comics Editor of Field Newspaper Syndicate, I made the acquaintance of a Brazilian-born cartoonist, Fernando da Silva, who was offered an assistant's job by Alex Raymond just prior to Raymond's death in an auto accident. Fred moved to the US anyway and became a leading advertising artist (working, among other commissions, in the style of Bob Peak on Marlboro cigarette print ads). When I met him he was drawing cartoons for Wrigley's Fun Facts, an innocuous strip of Believe-It-Or-Not type vignettes that ran in many Sunday newspapers (the final fun fact, of course, always hyping some aspect of a Wrigley chewing-gum product). Numerous surveys revealed that the Fun Facts feature was more popular with readers than many traditional comic trips. For a while, I entertained the idea of enticing Fred to draw an actual cartoon along those lines, instead of a cartoon ad masquerading as a syndicated feature. But of course my logic was faulty: Why would editors pay for a feature that attracted readers when they were already being paid good money to run a popular feature that attracted readers?
You can see (at least temporarily) an example of Wrigley's "Fun Facts" (subtitled "fun things to know and tell") from a Sunday [Louisville, Kentucky] Courier-Journal & Times published sometime in 1972 here (it's image 3 of the five-image series). Unfortunately, the image appears in a Craigslist listing and is not likely to last terribly long. I copied the image to my computer, however, and if I ever figure out how to post images in answers at EL&U, I will do so with this one.
Wrigley's "Fun Facts" strip was so popular that Xerox Publications published a collection of the strips in 1973 as Fun-to-Know Facts. Google Books lists a copy of this book, but the copy isn't searchable, even in snippet view.
In any event, I have used the wording "fun fact to know and tell" many, many times when dispensing trivia, and I've always considered the origin of the phrase to be the Wrigley's-sponsored Sunday comics feature/advertisement. A Google Books search finds relevant matches from as early 1984. From the "People" page of InfoWorld magazine (July 23, 1984):
More Fun Facts to Know and Tell: His real name is William Hawkins the Third, and when he was born, his grandmother said he was born in triplicate. Yes, folks, that's where the "Trip" comes from in Trip Hawkins, founder of Electronic Arts. ...
Did you know that ComputerLand started out as Computer Shack but changed after Radio Shack sued? This Fun Fact comes to you courtesy of Ed Faber, one of ComputerLand's founders, who was also honored at the Sybex bash.
Elephind searches of various newspaper databases yield matches for "fun fact[s] dating to the early 1970s. In a letter to the editor of the Columbia [Missouri] Missourian (April 20, 1974) from Bob Stone:
As I said I've been here six years and I have some fond memories. Such as back around 1969, give or take a few months, when construction began on the corner of College and Broadway and four years later you could still see them at it if you were lucky. And another fun fact about Columbia is that it seems whenever the utility companies need something to do, rather than improve service, they raise their prices.
Rush hour is about 30 minutes at the most. Another fun fact is that there are some people who want to put in parallel parking downtown. Have fun gang but remember to keep your collision insurance paid up.
There are many more fun facts about Columbia and I've enjoyed them all especially the people. Columbia, you've been a great town and I'll never forget ya.
From an advertisement for Schmidt's Beer in the [Ithaca, New York] Ithacan (October 14, 1976):
Make use of your useless knowledge in the First Annual (hopefully) Schmidt's Trivia Contest.
There are two kinds of intelligence. There's the kind that will make you famous, respected and a model to little children everywhere.
And there's Schmarts.
Well, the humanitarians at Schmidt's think your fun facts should do you some good, too. Ergo, the Contest.
And in JoAnne Goldberg, "Behrend Trivia," in the [Erie, Pennsylvania] Behrend Collegian (February 17, 1977):
It took only 20 minutes of reading for me to find out roughly 300 "fun facts" about Behrend College. Each week I will attempt to bring you such trivia.
All three of these matches are from college newspapers, which suggests that students may have been responsible for the initial spread of "fun fact[s]." Also of possible interest is Jim Fowler, "Between the Lines," in the [Houston, Texas] Rice Thresher (January 31, 1977):
You people had better be careful about what you say, especially those of you who don't know what I look like. I have the uncanny ability to overhear conversations at twenty paces, and you never know how such things might find their way into print. Of course those of you who have nothing worthwhile to say (and you know who you are, you who can only start a conversation by reciting a Wrigley's Fun Fact) have nothing to fear. I only steal good lines.
This instance unites college newspaper writing (the Rice Thresher was a student publication of Rice University) and the writer's still-fresh memory of Wrigley's "Fun Facts."
Elephind also uncovers a very localized but interesting outburst of "fun facts" from the 1950s. Mrs. Raymond Hoy, of Swenson, Texas, published a column in the Aspermont [Texas] Star called "News From Swenson," which several times began with the opening line "Fun. facts and folks" (note the midline period after the word "Fun," a typographical oddity that appears in all three instances of this phrase in 1950 and 1951 editions of the Aspermont Star that Elephind pulls up).
The expression "fun facts" seems to have made a lasting impression in Aspermont, because "Phoenix Club Entertains With Dinner on Saturday," in the February 14, 1957, Aspermont Star mentions that the expression was used as the name of a party game at the club dinner:
Mrs. T. C. Clark, president of the club, was toastmistress, and introduced Mr. Clark, who gave the invocation. A clever welcome set the pattern for "Fun Facts", a lively take-off on many of the guests, that was given by Mrs. Wesley Robbins.
Notwithstanding Aspermont's special claim to precedence in the use of "fun facts," it seems likely that this local usage had no wider effect and is unrelated to the rise of fun fact[s]" more than a decade later. (Elephind does not return any confirmable matches for "fun facts" between this 1957 instance and the 1974 instance from Columbia, Missouri cited above.)
Fun and fact[s] have been hanging around together since at least 1845 in the form of contiguous entries in lists of parallel elements. But fun fact[s] as a descriptive term appears to be a much younger expression. The earliest definite sighting of it that I've been able to confirm is from 1972, in "Fun Facts," a surprisingly popular series of comic-strip-like advertisements for Wrigley's chewing gum.
I remember reading that weekly feature in the Houston Post during the early 1970s, and I think (without definitive proof) that it may have been responsible for popularizing the term in the United States. Certainly its use as a synonym for "interesting bit of trivia" is entirely in keeping with the nuggets that the comic-page "Fun Facts" served up every week.
The earliest match for "fun fact[s]" in Google Books searches is from 1984. Elephind locates confirmable newspaper instances from as early as 1974, largely from college newspapers during that decade.
Elephind also scares up several occurrences of "fun facts" in a small-town newspaper in north-central Texas during the 1950s. These occurrences deserve special mention as being the first definite instances of the term's use, but they seem unrelated to the subsequent popularity of the phrase starting in the 1970s.
The historical record—or rather that part of it readily available to my miserly and sedentary wanderings—suggests that, however 'natural' the "fun fact" collocation may now seem, it was not employed in the sense provoking your enquiry (as I take it) until the middle of the 19th century. Then, in a slightly more periodic form, that is, as "fun, fact and fancy", the phrase was established and proliferated as the title of newspaper columns offering such tidbits to frivolous readers.
Digressing but a little, or "a bit", 'tidbit' itself may be the progenitor of 'fun fact', at least as expressed in the genetic line of sense. As the ancestor of 'fun fact', OED Online first attests 'tidbit' with reference to
A small and delicate or appetizing piece of food; a toothsome morsel, delicacy, bonne bouche.
["tit-bit | tid-bit, n.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/202556?redirectedFrom=tit+bit (accessed October 09, 2016).]
The quote cited in the OED conveniently defines the word:
(The Berkeley manuscripts, John Smyth, composed prior to 1640.)
From this auspicious beginning, 'tidbit' is soon (by the middle of the 18th century) employed figuratively with the special sense of
a brief and isolated interesting item of news or information; hence in pl., name of a periodical consisting of such items.
(OED Online, emphasis mine)
These 'tidbits', by the middle of the 19th century, were being collected and published in columns titled "Fun, Fact and Fancy". The earliest such column accessible with my limited resources was published in The Southern Standard, February 12, 1853:
These uses led to the eventual establishment of the idiomatic phrase 'fun fact' with the meaning first accorded to 'tidbit', that is, "a brief and isolated interesting item of news or information".