George C. Scott in The Day of the Dolphin (1973)

Jake Terrell (Scott) and his wife (Trish Van Devere) are researching dolphin intelligence and their relationship with humans. In the process of their research they've been able to directly communicate with one of them by teaching him English. Unbeknownst to them, there are radical right wing forces bent on destroying the President of the United States. They've learned of Terrell's dolphin and plans to use him and his mate to carry out the job.

Wikipedia

This film is directed by Mike Nichols and the screen play is by Buck Henry, so when I first started watching it I was sort of expecting a comedy - at least I was expecting some satire. Instead, it explores some of the more esoteric ideas about our relationship to other species in the setting of a political thriller. It's marginally successful at both, though tends to have a bit of a split personality.  

This film does not have a high profile, though it is remembered by some. It was nominated for two Academy Awards (score and sound) but has fallen into obscurity over the years. Above is a television commercial for a 1977 airing of it, uploaded to YouTube by robatsea2009

Obscurity factor: 7 (available on DVD, not largely remembered)

Whoopi Goldberg in The Telephone (1988)

Some films are obscure for a reason. You're probably imagining the worst, but let me put your mind at ease. One of the myriad reasons a film can be obscure is miscategorization. This film is really more a victim of that than it is a poor film in and of itself (though it's not exactly a magnum opus either). Whoopi Goldberg plays Vashti Blue, an actress living in a cold water flat in a bad part of town (what town we're not quite sure). She's been left high and dry by her boyfriend and her sleazy agent (Elliott Gould), she's besieged by her hostile neighbor and she's hanging on by one thin thread in the form of her telephone. It serves as her lifeline, her link to the outside world and she uses it constantly. As the story unwinds we learn just how lost she is as she tries to make the best of a bad situation.

Wikipedia

This film - the directorial debut for Rip Torn - is one of those that you either love or hate. It's a brilliant showcase for Whoopi Goldberg's crazy characters and she has some nice moments in it. It was, however, neither a critical nor a commercial success and I think that was primarily because, as I said above, it was miscategorized. At the time it was released, Goldberg was becoming well known for her work as a comedian, and appearing in several big budget formula films like Jumpin' Jack Flash (1986) and Burgler (1987). This independent film was a departure in concept, but not in marketing. Like other flops, it was presented as a zany comedy, while it's really a psychological drama and a character study. Regardless of how you feel about the film, if it had been marketed more aptly and the timing of its release hadn't come when Goldberg was becoming known for more conventional fare, it might have been better received. Look for John Heard in a cameo toward the end.

The Telephone is available on VHS and DVD and can also be found in full on YouTube. The uploader has disabled embedding, so you'll have to go directly to the video here. Above is a clip from the film featuring several of Whoopi's characters uploaded by celestialboy80.

Obscurity factor: 8 (on DVD & YouTube, largely unknown)