Secret Honor

"Secret Honor" (1984)
Director: Robert Altman
Who's Giving The Solo Turn And Why? In a rare early lead, Paul Thomas Anderson favorite Philip Baker Hall plays a fictionalized version of Nixon, experiencing a long, dark night of the soul in an increasingly ranting, alcohol-fueled diatribe/confessional/reminiscence/memoir of his life before his spectacular fall from grace. Based on the play of the same name.
Who Does He Interact With, Then? Practically speaking, purely with a bottle of scotch, a loaded gun and a tape machine, but essentially the monologue feels like it's rhetorically directed at times at a putative version of The American Public, at other times at his mother or his assistant Roberto, or a judge, or really, any of many other players in the story that a tangent brings to his mind.
Does It Jump The Shark? A little, when, SPOILER ALERT having spun so many exculpations and excuses, Nixon suggests that he himself was behind the Watergate leak, as his Presidency had become so corrupted by entrenched interests that falling on his sword was the noble thing to do. The portrait of Nixon drawn to that point has been compelling enough, equal parts egomania and intelligence, and arguably the new take on the Watergate conspiracy is a twist too far. SPOILER ENDS
Is It Any Good? It's stagy, no doubt and definitely only for those with a working knowledge of, and a ready interest in, that period of politics (references are made, sometimes on a first-name basis, to the staff at the time of Watergate, for example—allusions it would be easy to miss if you're not already familiar). That aside, Hall delivers the kind of performance for which the word "titanic" was coined, and if no scenery is left unchewed, still it's a brilliant portrait of a sclerotic Nixon rendered as an epic poem, a Viking saga of guilt, blame, rage, and possibly even encroaching dementia.

Swimming to Cambodia

"Swimming to Cambodia" (1987)
Director: Jonathan Demme
Who's Giving The Solo Turn And Why? Spalding Gray, as it's a filmed version of his one-man-monologue/theatrical play, as are his two other features "Monster in a Box" (dir: Nick Broomfield) and "Gray's Anatomy"(dir: Steven Soderbergh).
Who Does He Interact With, Then? No one really, though there's a live audience present, some maps behind him, occasional clips from the film "The Killing Fields" and Gray often looks straight into the camera to, giving the impression of no fourth wall.
Does It Jump The Shark? Not at all. In fact, Demme's approach is subtle but perfectly suited to the filming of what is essentially a raconteur, um, raconteuring. Gray's mastery of the monologue format, unfashionably austere though it might sound, is such that time flies by, much as it did when seeing him perform live, and the narrative he weaves never ceases to surprise and engage.
Is It Any Good? Because of the style of film it is, it's definitively not for everyone, and yet it's much more accessible than you might think. It's Gray's account of his involvement with the Roland Joffe film "The Killing Fields," but it's also about his dawning awareness of the war in Cambodia and the grotesque human cost of it, poignantly and often hilariously counterpointed with his reminiscences (truthful "except for the banana," he claims) about the brothel visits and drug trips and celebrity encounters that also characterized his time on the shoot. Gray's field of expertise was narrow, but he absolutely dominated it, and it's easy to see why, when the purity of a guy sitting with a notebook and telling a story can be, to some of us anyway, as riveting as the biggest-budget tentpole. And Demme's skillful camerawork and editing (that keeps in some of the fluffs that Gray makes in the course of his fast-paced speech) are the unobtrusive, unsung heroes of the piece.

All Is Lost

"All is Lost" (2013)
Director: J.C. Chandor
Who's Giving The Solo Turn And Why? Robert Redford plays the unnamed solo sailor who has to battle the elements adrift thousands of miles away from land in a damaged sailboat.
Who Does He Interact With, Then? The elements, mainly, and the rigging and supplies found on his boat as he meets each new challenge with a resourcefulness that never underestimates the difficulty of the situation or exaggerates his abilities. Occasionally he attempts to reach someone over the radio, or to attract the notice of a passing ship, but mostly Redford is reacting, dialogue-free, to whatever new way the ocean is trying to kill him, with the brief exception of a prologue, which is him reading a terse farewell note in voiceover to his family.
Does It Jump The Shark? Amazingly, no. While lesser one-man shows often lapse into telling, not showing, the bruising story of "All is Lost" feels exceptionally real and is all communicated through action and visuals, and while Redford's performance is incredible in a physical sense, the film is so uncompromising in refusing to sentimentalize or even particularly dimensionalize him, that he becomes almost an abstraction by the end: the embodiment of the survival instinct, without us knowing what or who he is surviving for. 
Is It Any Good? Terrific. "Locke" is almost unusual, these days, for being a one-man show that isn't also a survival story (though we guess he is kind of fighting for moral or psychological survival during that car ride), but "All is Lost" is absolutely about a pared-back battle for existence, and is in its way possibly even more rigorous than "Locke." There has been a glut of superior survival movies of late ("Gravity," "Captain Phillips," "A Hijacking" all qualify) but arguably this is the one that does the most with the least, and while Redford deserves, and receives, huge props for the grueling part he played, it is a magnificent achievement for Chandor, especially.

The Noah

"The Noah" (1975)
Director: Daniel Bourla, his only directorial credit.
Who's Giving The Solo Turn And Why? Usually relegated to comic relief sidekick parts, probably because of his tall, burly build, lugubrious face and deep gravel-driveway voice, actor Robert Strauss takes the title role here as the literal last man left on earth, a soldier who has survived a nuclear war. It was his last role, as he died just a few months after the film got its brief release, seven years after it was shot.
Who Does He Interact With, Then? He mostly interacts with imaginary people, who are heard as off-screen voices and to whom he reacts and converses as though they were real, specifically a companion/servant called Friday, a woman called Anne-Friday and eventually a young boy, then a classroom of children, then a whole army. 
Does It Jump The Shark? Sadly yes, though it's difficult to say quite where—probably the point at which he goes charging off into the jungle brandishing an axe to kill the imaginary Friday and Anne-Friday, whom his paranoia has decided are coupling up and talking about him behind his back. Or maybe when the religious subtext goes a bit textual and Noah turns Moses.
Is It Any Good? Not really, though it is again a curious experiment, and the ambition can't be faulted. Strauss is remarkably committed but the film is just too long, the script is too blunt, and the jittery camerawork, that often switches angles abruptly to indicate that Strauss is "talking to" some other new imaginary interlocutor, gets very distracting, very quickly. But there is a black-and-white grandeur to some of the photography, a perverse WTF weirdness to some of the more deranged scenes, and if you manage to stick with it for long enough, the quiet of the ending, after all the noise and chaos, is surprisingly elegiac and affecting.