When was the expression "road movie" first applied to a film?

I think that "road movie" didn't gain traction as a descriptive term for a genre of fictional films until the late 1960s or early 1970s. The movies associated with it at that point were (most crucially) Easy Rider (1969) and (secondarily) Two-Lane Blacktop (1971). Wikipedia cites Bonnie and Clyde (1967) as another key movie in the genre, but I think that view is a bit of a stretch; in my view, it would be more accurate to call Bonnie and Clyde a "crime spree film."

Although movies set largely on the roadways—such as the trucker-focused films They Drive By Night (1940) and Thieves Highway (1949)—or examining alienated young people on wheels—like The Wild One (1953)—or dealing with interstate crime sprees—like Gun Crazy (1950)—had been screening for decades, the descriptive term "road movie" as a plot genre did not become popular until significantly later.

Literal 'road movies': Documentaries about roads

It is certainly true that older nonfiction movies about highway or road construction were sometimes termed road movies or highway movies. Such films are mentioned in, for example, Ontario Ministry of Transportation and Communications, M.T.C. Report No. RR., issues 137–155 (1967):

The final testing of the selected route can be carried out by a road movie, seen from the driver's eye, along a designed roadway whereby the vertical alignment is combined with a three-dimensional layout.

and earlier still in Proceedings of the Annual Convention of the American Road Builders’ Association (1940):

We have a park movie which is sent out to clubs and is booked for about 100 meetings a year. It emphasizes highways, though it comes under the classification of parks. This year we plan to make our first highway movie, which will portray problems of road building to the people in a lay fashion and will also show them the roads of 25 years ago contrasted with those of today.

The term "road film" seems to have been somewhat more common than "road movie" for these productions. One example appears in "The Motion Picture Film in Highway Bond Campaigns," in The American City (February 1920):

One of the most telling points in the road film soon to be released is a story which was picked up showing how one hard-surfaced road has been the means of consolidating five isolated, one-room school-houses into a modern consolidated structure.

However, these industrial road-making movies have no relevance to the later genre name.

Another seemingly literal use of "road movie" appears in Ron Delpit, "My Side of the Story," in the Madera [California] Daily Tribune (October 13, 1965):

Each year the World Series brings together a group of participants that are about as compatible as dynamite and a match factory.

The 62nd annual soiree has proved to he no exception.

Los Angeles employs the services of some well-traveled hands who have seen more scenery than an old road movie.

This article is about the Los Angeles Dodgers, which were playing (and trouncing) the New York Yankees in the baseball World Series that year. The Dodgers were a veteran team, a point that prompted the writer to equate their familiarity with passing scenery to "an old road movie." The comparison is odd and seems to exist in a vacuum; at any rate, I don’t find any other references to "road movies" in the sense (seemingly) of footage captured out the window of a moving vehicle.

Goofy 'road movies': Carry on, Bob & Bing

As rjpond's answer notes, Bing Crosby and Bob Hope appeared in a series of seven semi-romantic adventure/comedy films between 1940 (The Road to Singapore) and 1962 (The Road to Hong Kong) that had in common (besides frequent appearances by Dorothy Lamour) the words "Road to" or "The Road to" at the beginning of their titles—and these films did become widely known as the duo's "Road" movies. Strictly speaking, however, these are not "road movies"—they are "buddy films." Ultimately, associating Hope and Crosby with the modern understanding of the term "road movie" makes about as much sense as linking "Carry On" gang films with the concept of carry-on luggage.

Literary 'road movies': A genre of fictional films

The first Google Books match for "road movie" in its fully evolved modern sense is an item in Newsweek magazine, volume 78 (1971) [combined snippets]:

Actor's Actor

His life has wandered like a road movie, and now a road movie called "Two-Lane Blacktop" has turned that life around, lifting 42-year-old Warren Oates from the swollen ranks of capable character actors to the edge of swollen ranks of capable character actors to the edge of stardom. As GTO, the unhinged drifter who sails about America picking up hitchhikers and adopting their psychic coloration, Oates clinched his standing as a superb character actor, an actor's actor, a judgment confirmed by his tough and sensitive performance as Peter Fonda’s lonely comrade in "The Hired Hand."

This instance occurs within a year of the first OED match for the term from late 1970 in the New York Times (as mentioned in rjpond's answer). But given that Newsweek wasn't (and isn't) at the forefront of cineaste culture, you’d have to think that by the time the genre term "road movie" showed up there, it had already been floating around in popular culture for some time.

A slightly earlier instance of the related term "road picture" appears in a review of Goin' Down the Road (1970) in Motion Picture Herald (1970) [combined snippets]:

Goin' Down the Road [R] Chevron Pictures — Phoenix Film, Inc. "Goin Down The Road" is an impressive achievement — a product of Canada's youthful and growing film industry. The film, Donald Shebib's first feature-length effort as director was also produced and edited by him for a total cost of only $82,000. Originally filmed in color in 16mm, the film might be described as Canada's "road" picture, as it does resemble "Easy Rider" in some ways, "Goin' Down The Road" presents its protagonists as victims of shattered dreams promoted by a mass-media urban culture which is often insensitive to human conditions and problems. However, its characters are trying to live within the system rather than outside of it.

This review probably antedates the New York Times's December 6, 1970, instance of "road movie." The term used here is slightly different, but its meaning is clearly the same. The example provides further evidence that Easy Rider served as the archetypal "road movie" as that genre emerged.

An early instance of 'road movie' in film criticism

The most interesting early instance of "road movie" in the Google Books search results is the one in the 1953 issue City Lights magazine. Multiple followup Google searches reveal that the article in which it appears is Jordan Brotman, "Ace on the Road: Kirk Douglas and Hollywood," in City Lights issue 4 (Fall 1953) [combined snippets]:

The Kirk Douglas movies, taken alone, give us hopeless feelings about liberalism in Hollywood, at the same time that they raise a very real, involuntary hope that keeps us in an unpleasant suspense. The road movie, in its original form, came to an end with the entry of the ace on the road. But no idea, no form, is ever permitted to stand still: sooner or later, an ace was going to get on the road, a new moral threat would challenge the idea to grow greater by encompassing it. The idea, we see, surrendered some movies ago. ...

1953 POSTSCRIPT: Since this article was written (I951), three new Kirk Douglas movies have appeared. Two of them are milestones of a sort. THE JUGGLER (l953) is a highway movie set not in America but in Israel, where it transplants, by a kind of cultural imperialism, the social bleakness of ACE IN THE HOLE. DETECTIVE STORY (l952) celebrates the marriage of Kirk Douglas and the Broadway theatre. This was inevitable. Broadway, in its senescence, must have rejoiced in the show of strength provided for the stage by Kirk; we can only guess at Kirk's feelings on gaining this high preserve of cultural respectability.

This excerpt is interesting for several reasons, perhaps the most striking of which is that, although Brotman is interested in "the road movie" as a cinematic archetype, his preferred term for the genre is "highway movie." This becomes clear when we look at the opening paragraphs of the piece:

Among all the developments that changed the face of the Hollywood movie after the war, two must be singled out for the strong and contrary influences they have sought to exert over our lives. One is the rise of a new kind of film, based on part of the common experience of postwar life. This is the "highway movie": it gave us most of the best pictures of the late 40's. The other is the rise of an undistinguished actor named Kirk Douglas, now an established name in Hollywood. Kirk Douglas carved out his career in the highway movie and decided its fate. ...

If we were to try to pin down the distinctively American quality of so many good postwar movies – KISS OF DEATH, CHAMPION, THE PROWLER, RED RIVER - we should soon come across the fact that all of them were dominated by an image: an image of the American road. The road, the great theme of both our geography and our inner lives, has been faithfully, and as it were involuntarily and painfully reflected in our pictures. Think of RED RIVER, the story of a cattle exodus from Mexico to the Abilene railroad. With its primitive subject, RED RIVER only gave us our broadest land-bearings: yet these could never have been transformed, as they were, by such sensitive devotion to every inch of the way, by such a hunger to consume distances, if we were not in the habit of seeing the roadstead and the highway as part of our most personal, unhistorical selves.

This link, between the road and ourselves, is the emotional clue to many successful movies of the late 40's, like SUNSET BOULEVARD. Strip SUNSET BOULEVARD to its essential situation, and you have William Holden racing through Los Angeles a breath ahead of the finance company - a down-and-out film writer in a city of highways, terrified at the thought of having his car taken away from him. There is something momentous about this escape, not only because we all know Los Angeles, but because there is a Los Angeles of the mind, and William Holden flitting like a moth from road to road down to the oldest road in civilization – Gloria Swanson’s stately, decayed boulevard – becomes Theseus in an American labyrinth.

In such pictures as this, the discovery of the highway gave the movies a new dramatic grasp of the careers of men, their rise and destiny. The "career" is preserved in its literal sense, as a rushing over a road – even in big-city movies like KISS OF DEATH. A hero is forced out of the common life and travels his life alone.

The sources of the highway movie – with its moral intensity, its manneristically severe photography – can be traced to any number of traditions: the suspense film, the tough detective film, the American-at-war film, and furthest to the Depression film and the documentary. But these are not all. Hollywood’s central tradition derives from its audience.

I have grave doubts about the legitimacy of Brotman's assertion that "highway movies" were something new under the sun in the postwar world. One can scarcely deny the highway theme of Sullivan's Travels (1941), for example, or its direct dramatic antecedent I Am a Fugitive from a Chain Gang (1932). Brotman seems likewise oblivious to the essential role of the road (and the railroad) in The Grapes of Wrath (1940). Even the western had an early highway epic in the form of Stagecoach (1939), nine years before Red River reached the screen. And what is The Wizard of Oz (1939) if not a "highway movie" set in a world without internal combustion engines?

But be that as it may, the relevant points here are that Brotman's essay identifies the metaphor of the road as central to an American mythos that serious American films, at a certain point, embraced wholeheartedly—and that he seems to have coined the term "highway movie"—and (incidentally) varied it at one point as “road movie”—to describe this genre.

Is Brotman's essay the source of "road movie" as a genre name? On first consideration, it seems absurd to suggest that an essay in a little-read art and poetry magazine could have had such influence. However, contextual information lends at least a little more weight to the possibility. As noted earlier, the essay was written in 1951 and published in 1953 in City Lights, a San Francisco periodical associated with Beat poet Lawrence Ferlinghetti, who also co-founded San Francisco's City Lights Bookstore in 1953. According to Wikipedia, Jack Kerouac conceived the Beat classic On the Road in the late 1940s "and then typed [it] out on a continuous reel of paper during three weeks in April 1951"—although the novel was not published until 1957.

I don't think it is at all far-fetched to imagine that these Beat emigres from New York and other points East to the Golden West had a soft spot, if not a preoccupation, with "the road" as a quintessentially American symbol of adventure, hope, and self-discovery. Kerouac's book, which follows semi-aimless artsy-drugsy protagonists as they drift westward across the United States, was extraordinarily popular with an audience of aspiring hipsters and alienated youth—people who didn't yet know that they would eventually become middle managers at large corporations.

Conclusion

Whether Jordan Brotman's use of "highway movie" and (in one instance) "road movie" in his 1951/1953 essay "Ace on the Road" had any direct (or indirect) impact on subsequent cinematic terminology is certainly debatable, although I imagine that in Beat coffeehouse culture the essay was widely discussed. Realistically, popular consciousness of the term "road movie" in its modern sense seems to have occurred no earlier than 1970 or 1971.

The immediate need for a descriptive label for what became known as "road movies" was almost certainly due to the phenomenal success of Easy Rider (1969)—an extremely influential youth film that became a defining artifact of 1960s counterculturalism.

Jack Kerouac's novel On the Road, meanwhile, deserves a lot of credit for making impulsive, vaguely defined quests seem cooler than cool to members of a commercially desirable movie-going demographic—and once a cool plot line has resonated with the public, a mountain of screenplays is sure to follow.

@jejorda2 noted that an earlier term for "road movie" was "road picture". If we count this then I found this in What's Happening in Hollywood (1944)

Paramount has promised another "Road" picture, reuniting the threesome - Bing Crosby, Bob Hope and Dorothy Lamour...

And Motion Picture Daily in 1945 asked (of the movie Road to Utopia):

How does this "Road" picture compare with others?

The earliest occurrence for "road movie" cited in the OED is from 1970: 1970 N.Y. Times 6 Dec. 26/7

The ultra-with-it company that has manufactured more ‘road’ movies than you could shake a motorcycle at.

Unfortunately the OED doesn't tell us which movies were being referred to. Perhaps someone with a NYT subscription could check the archive.

"Road movie" was used pre-1970 but in a different meaning ("The final testing of the selected route can be carried out by a road movie, seen from the driver's eye, along a designed roadway whereby the vertical alignment is combined with a three-dimensional layout" - Ontario Ministry of Communications 1967).

Google snippets also show some pre-1970 results that might exemplify the modern usage of "road movie", but it's hard to tell because Google only makes small portions of the text available:

The road movie, in its original form, came to an end with the entry of the ace on the road.

City Lights Issue 4, Page 52 (1953)

...the performances are slick and clever, and also abundantly endowed with that special veneer of studied nonchalance that Crosby and Hope perfected in their Road movie ducts.

Saturday Review Volume 47 p44 (1964)