BACK TO THE FUTURE (1985)
This film was plagued with problems, and was barely marketed at all.
Eric Stoltz was originally cast as Marty McFly, but was dropped early in the filming process when his version of Marty was too serious and not funny.
Michael J. Fox was a much better Marty, but his commitments to "Family Ties" left him unavailable to promote the movie.
Studio executives were also concerned about the "inappropriate" plot regarding a mother falling in love with her future son who traveled back in time. One was especially disturbed by the line on a film poster, "Are you telling me my mom has the hots for me?"
Most studio executives thought the film would produce middling results, and decided not to spend much money promoting it, especially because of Fox's unavailability.
They were shocked when test audiences universally loved the film, but it was too late to invest in much promotion. Instead, they moved up the release date to early July and prayed that word of mouth would save it.
I stumbled upon Back to the Future on its opening day, as a 13-year-old. My friend and I went in to see it, knowing nothing about it besides it was something about time travel and featured Michael J. Fox. The theater was half empty.
We walked out saying how awesome it was, and wondering why we hadn't heard of it before.
Indeed, this was the typical experience around the country, and great word-of-mouth quickly spread. The second weekend was bigger than the first, which is very uncommon for a hit film, and Back to the Future ended up becomng wildly successful.