A lot of people probably don’t know it, but when the superb Swiss actor Bruno Ganz, who died Friday at 77, took on the role that brought him his greatest jolt of fame, playing Adolf Hitler in “Downfall,” it was one of the most paradoxical casting choices in modern movies. Ganz, portraying Hitler in the final days of World War II, when the Führer was trapped in his bunker (and, more than that, in the implosion of his evil dreams), did an impersonation of Hitler at his most full-throttle fulminating. The performance was raging, antic, operatic, possessed; it was true homicidal acting. (That’s one reason why “Downfall” became the movie that launched a thousand Hitler Internet memes.)

Yet up until then, that kind of smash-mouth volatility had almost nothing to do with the persona of Bruno Ganz. He was sly, pensive, puckish yet woeful, inwardly commanding, almost always intensely becalmed, an actor with a light in his eye that could radiate anything from merry deviousness to the fiercest of existential distress. At times, Ganz exuded a Continental version of the qualities we associate with Willem Dafoe — haunted yet beatific, with a worldly benevolence. In the last film I saw him in, Lars von Trier’s “The House That Jack Built,” Ganz played a kind of all-knowing metaphysical guardian-angel head shrinker for serial killers, and if that sounds loony tunes (okay, it was a Lars von Trier film), the wonder of Ganz’ performance is that he sold it and you completely bought it. He played the character as a variation on his specialty, a spirit wanderer who knew all about the darkness yet remained, in a hard-won way, on the side of good.

It was that rare ability to navigate morality from opposing angles that made his Hitler so mesmerizing. By the time “Downfall” was released, in 2005, a great many actors had taken a crack at playing Adolf Hitler, but Ganz may have been the first to totally nail him in body and spirit, mood and gesture. He took off from the gnashing tyrannical mesmerist we saw and heard in Hitler’s recorded speeches, but in “Downfall” this was a dictator fueled by the drug of his own delusions, his hand held trembling behind him, his mind convinced that the German forces, though they appeared to be losing, would launch themselves to victory at any moment. Ganz offered a disquieting portrait of the “civilized” side of Hitler (the baby-cheeked smiles, the studied courtliness around women and children), but then he descended into spitting arias of rage, and the result was a true study of evil, of grandiose paranoia inflated into a worldview. Ganz dramatized how Hitler built his anger into a force field, shutting out anything he didn’t want to see. The performance was epic, but in its uncharacteristic way it was pure Bruno Ganz: a shot of humanity where you least expect it.

He’d been doing that, albeit quietly, for many decades, notably in the other role that brought him the most attention: that of the hovering, gently heartbroken angel in “Wings of Desire.” I’m not one of those people who think that Wim Wenders’ 1987 symphony-of-Berlin tone poem is a masterpiece (I find it more windy than entrancing, and often a bit twee), yet it’s a film I’ve gone back to simply to gawk at Ganz’s acting.

As Damiel, one of two angels who wanders through a black-and-white designer dystopian Berlin overhearing the thoughts of mortals, sometimes ushering them into the great beyond, Ganz, in his long black coat, wore a look of the most complicated compassion I have ever seen. The character has plenty to say, but in essence what Ganz does verges on silent-movie acting. As a benevolent force, a presence, he is unparalleled, and there are moments — like the one where he coddles a man on a subway — that the film becomes as elemental in its tenderness as “Eleanor Rigby.” That’s because of Ganz, who we can believe would swoon over a French trapeze artist (played by Solveig Dommartin) enough to want to give up his wings and join the human race.

For a long time, Ganz was the middle-aged poster boy of Eurocentric angst, skulking through the war-torn Middle East of Volker Schlöndorff’s “Circle of Deceit” or the nightmare miasma of Werner Herzog’s “Nosferatu.” His features acquired a certain battle-scarred worldliness that he never lost, and his receding hair became his trademark — the sign of someone always thinking, maybe a bit too much. (The first time I ever saw him, it was when he played a computer-scientist-turned-neurotic-chess-master in Wolfgang Petersen’s 1978 German TV movie “Black and White, Like Day and Night.”) Ganz could always be counted on to tone up the proceedings with a certain cultivated old-world panache in Hollywood films like “The Boys of Brazil” or, later on, “The Manchurian Candidate” and “The Reader.” But for many of us, the role that defined Ganz, and remained in many ways his greatest, was that of the ailing picture framer in Wenders’ “The American Friend.”

Hitchcock famously made movies about “ordinary men in extraordinary circumstances.” The great film noirs were often about everyday saps, like Fred MacMurray’s insurance salesman in “Double Indemnity,” who were drawn into spider webs of vice and murder. But was there ever a killer more ordinary, more rivetingly unremarkable, more one of us than Ganz’ Jonathan Zimmermann?

“The American Friend” is based on a Patricia Highsmith novel (“Ripley’s Game”), and the whole mechanism by which Zimmermann, a family man who is battling leukemia, gets roped into committing a pair of gangland murders may strike you as a bit rickety. (In essence, his illness is used as a form of blackmail.) But you stop questioning what happens the moment this poor nobody picks up a gun and begins to track an American gangster through the corridors and escalators of a Paris Métro station. It’s every thriller you’ve ever seen made dizzyingly down-to-earth and real, and what seals the off-kilter but hypnotic movie-but-not-a-movie quality of it is Ganz’ acting — the fear and trepidation in his dark-eyed stricken-puppy-dog stare (he was just 35 when the film was shot), the insecurity and desperation that guide his every amateur move.

And then, after he bumblingly executes the hit and is ordered to do another one, something remarkable happens. The crimes he’s committing, though he doesn’t get any more professional at them, begin to ignite the dying spirit inside him. Does everything work out? Not entirely. Yet the movie, on the wings of Bruno Ganz’ performance, takes you to a place that’s at once quietly saddened and staggeringly alive. He was the rare actor who, even when tethered to the earth, found a way to soar.