What happened to the idea of art films? Great question, and since it's got me thinking, let me dare a full post instead of a comment. I'll argue that, first, film became accepted as art, including mainstream film. Second, an outsider venue for art films became less crucial, thanks to video. But could those assumptions be changing as money centralizes yet again? NOTE ADDED: You'll see that I embellished this, because I wasn't satisfied with how it ended.
I think a couple of things happened to art films. First, the term dates to a time when film as an art was an open question. Moreover, answering that question favorably seemed at first to hinge on an opposition to Hollywood films. There were art films, mostly European, and art houses, to show them.
But people got more comfortable taking film seriously. In addition, François Truffaut's auteur theory in France and Andrew Sarris's American Cinema at home made it clear that the mainstream had long competed with what Europe can do. A new blast of American film in the 1970 then seemed to settle matter. So did Pauline Kael's championing of their grit, as in her classic description of the ending of Bonnie and Clyde, but also in her admiration for even better directors, such as Martin Scorcese, Rober Altman, and Francis Ford Coppola. I'd vote for the first two Godfather films as the only other movies to compete with the sense of tragedy in Orson Welles at his best. 
As one last twist, another round of revisionism championed something that might have seemed even schlockier than the previous target for champions of European art film, film noir. I've my doubts about Billy Wilder and rest, so there. But there was a move toward this view in France as early as Truffaut's and Sarris's glory days. Think of the style and quotes in Jean-Luc Goddard's early movies and Alain Robbe-Grillet's novels. It's ironic that an arty European film last year in turn quoted the race through the Louvre in Goddard's Bande à Part
If art film lost ground as a context, the art house and other walls between types of theaters seemed to lose value, too. Multiplexes and conglomerates drove them out from one side, the top down, but so did video rentals and sales from the other side, the bottom up.
It's interesting to wonder, though, whether art movies are having a comeback. Is the growth of the small studio within the large one or the success of Harvey Weinstein's productions a last attempt to fend off the inevitable failure of big money? Has it already happened with this dreadful summer of Jennifer Anniston and Johnny Depp? Commercial pressures are worse than ever, more good stuff has been coming from outside the United States over the last couple of years than ever before, and lots of small movies play only in smaller venues (like the Angelica, say, in New York).
Stranger still, almost as soon as I got used to video (and before I have the capability to download whole movies myself, films I want to see may now never turn up at local video stores. Forget imports from the Third Word: stick to Western white males. I've been wanting to rent a version of The Cherry Orchard from about three years ago, and I can't. I've wanted for ages to see Alfred Leslie's movie about the Cedar Bar, in the days of the great American painters, and that one went straight from a Tribeca film festival (sold out) to the library of MOMA. I may eventually have to pull press privileges and beg his gallery (Allan Stone) for a look.
And, speaking of galleries, then there's real video art, while video stores are renting TV shows. When Douglas Gordon's 24-Hour Psycho shows the entirety of the Alfred Hitchcock classic in slow motion, it plays at MOMA, and I can't rent a copy, then where are we? Maybe the wheel will turn yet again!
NOTE ADDED. If it does, where will it stop? Perhaps one successor to art films took possession some time ago: instead of art films, think of cult films. Almost anything can become a cult classic, past or present, and it does not even require broad consensus. If enough people consider M. Night Shyamalan, The Matrix, or even Tim Burton a cult classic, perhaps they can. After all, what else makes a cult in any field, by definition?
The change reflects the loss of a modernist canon and the growing dominance of a market model, with freedom of choice, even as it rebels against the choices offered. It reflects the acceptance of popular culture and of even art’s role as entertainment. It parallels the term indie in music, and indeed one does speak almost interchangeably of independent movies, not necessarily solely as defined by independent channels of production and distribution.
It may not resolve all my qualms either. It may not make films of marginal gross more generally available. It may retain some of the worst biases of mass entertainment after all, as in catering to the tastes of teen and post-teen males. Somewhere, however, in the space between small studios, cult films, art video, and others, there may yet be room for the movies.