Charles Foster Kane's first action after acquiring the New York Inquirer is move into the editor's office (quite literally, as his two offsiders move all his belongings in there), because "news happens twenty-four hours a day". Within a few years he became the sad fat man everyone remembers, but damned if young Kane isn't the closest 1940s drama heroes get to Crazy Awesome.
Captain Jack Sparrow, who, by the third movie is certifiably off his rocker, if only there were someone to certify him. Jack got most of his good ideas in the film from his hallucinations. Of himself. Lampshaded in the third movie..
The other captain of the Black Pearl, Hector Barbossa, is pretty Crazy Awesome himself. For example, in the third film, he intentionally gets his own ship hopelessly lost in order to find the "World's End"... and does so, followed by sailing it off the edge of the planet into the Netherworld, while laughing like a maniac, with an "arr" or two thrown in just for giggles.
If ever there was a museum dedicated to Crazy Awesome, one exhibit would have to be the remains of the mental ward in One Flew Over The Cuckoo's Nest as seen the morning after the party, as a testament to causative agent Randall P. McMurphy, virtually a god of the trope.
By the same token, most any comedic Jim Carrey character, and some of the dramatic ones, too.
Any character in Kung Pow!, but in particular The Chosen One ("You killed my family, and I don't like that kind of thing!"), Master Tang ("Let your anger be as a monkey in a piñata, hiding with the candy, hoping the kids won't break through with the stick!") and Betty ("Ngggg!"). Also, The Cow.
The movie's true Crazy Awesome moment is when the love interest tries to comfort Chosen One by, amongst other things, putting salt and mercury on his bloodied hands and lighting them on fire before asking him to rub it in her hair to which he replies "You just get stranger and stranger and stranger." The next days, his hands are somehow tough enough to remove the metal caps from the dummies he was practicing on and he declares "You have helped me reach the next level, and I was beginning to think you were just a sadistic psycho-bitch" to which she replies "Aiyaiyaiyaiyaiy"
Pick a Rajnikanth movie. Any Rajnikanth movie. He makes Chuck Norris look feeble.
Gonzo: What are you doing? The airport's over there! (points to his left, across many parallel roads)
Duke: Don't worry. I've never missed a plane yet. (does a ninety-degree turn and drives across desert terrain and about three lanes of traffic, crashes through the fence around the airport, dragging part of it with him, and pulls up beside the plane)
The new incarnation of James T. Kirk. He cheats The Kobayashi Maru, convinces his best friend to sneak him on board the Federation flagship whilst grounded for cheating said test, gets himself promoted to first officer, provokes Spock into abandoning his post as acting captain, and then throws approximately eight billion lives into the hands of one questionably sober but undeniably brilliant engineer. And then he saves Earth. And then he jumps from Cadet to Captain of that same Federation flagship within, at most, two years, meaning he is at least a half-decade younger than his TOS counterpart—who was also the youngest Captain in Starfleet history. Yeesh. Refuge in Audacity much? But hey—he did better.
Staff Sergeant William James in The Hurt Locker. He keeps parts from bombs he's disarmed—but only from the ones that almost killed him. At one point, realizing how big the bomb he's trying to disarm is and that even with the disposal suit he would die if he screwed up, he takes it off (noting that "If I'm gonna die, I'm gonna die comfortable", and flipping ff his superior officer when ordered to put it back on). With some of the stuff he pulled, if he weren't such a genius at the job, he...well, he'd be dead.
Buck of Ice Age. Nothing he says makes sense... and yet he somehow makes it make sense with how he's the only mammal in the entire underground world he's in. Just get past the fact that he's married to a pineapple...
While every member of the Sprocket Holes, as well as Cecil himself, is this, the one who really takes the cake is Raven, one of about three of them who gets away from the cops alive, by hiding in the back of a hearse.
Sorry, but Satan says you need more color!
Sir John Talbot, From the recent reimagining of The Wolf Man. He's essentially a very British Gentleman Explorer, Except old and really, Really Crazy. He takes on a werewolf in single combat, Unarmed. That is all.
The major motion picture version of Cloudy with a Chance of Meatballs has two: one as Earl—that is his name, yes?—and the other, Manny(?), as non-crazy but technically fitting variation.
The A-Team: The whole team specializes in this, but special recognition goes to Howlin' Mad Murdock.
A Real Life example from a film is Andre Gregory playing himself in My Dinner with Andre. If he wasn't Crazy Awesome it might be just another boring dinner conversation.
Sgt. Hugo Stiglitz. The man took out thirteen Gestapo officers! All by himself, while sporting a most awesome bitchface.
Dr. Praetorius (Ernest Thessiger) from Bride of Frankenstein is a Camp GayMad Scientist who grows tiny people in jars, does not so much tinker in God's domain as wage open war against him, dreams of creating a race of monsters and interrupts his grave robbing to hold cozy picknics with Frankenstein's monster in the crypt. To put it another way, this is a Mad Scientist who scares Dr. Frankenstein.
Marvin Boggs in the film adaptation of RED is a combination of this and Properly Paranoid, Crazy-Prepared, and Crazy Survivalist. His definite Crowning Moment of Awesome is when he accurately guessed a seemingly helpless woman was actually tailing them, and then later faced her down as she fired an RPG directly at him. He blew up the projectile in mid-air with a perfectly aimed bullet.
Dolemite. In "The Human Tornado" alone, he makes threats in rhyming verse, shoots a car with a shotgun (causing it to explode for no reason), and then proceed to carjack his way to California from the other end of the US. Other moments include fight scenes wherein he just makes (literally) random grunts and other silly noises in an attempt to… intimidate?
Indy's father in the Last Crusade. The old man took out a Nazi war plane with a flock of seagulls and an umbrella.
RattlesnakeJake from Rango. Why? He's a gunslinger who doesn't have any arms, so he has replaced his rattle with amachine gun. He's a damn good shot with it too.
The titular character (played by Johnny Depp) in Don Juan DeMarco is subject to a persistent identity delusion... which brings happiness to him and everybody in his vicinity. So does his condition really need to be cured?
Realistically used in Teachers, in which the most popular and effective history teacher in the school dresses up as historical characters for lectures and has students role-play key events of the past. It's eventually discovered that the guy isn't actually a teacher at all, but a mental patient prone to adopting the personas of those around him.
Boris 'The Blade' Yurinov from Snatch is a crazy Russian who just won't stay dead. Well, technically he will, you just have to kidnap him, throw him in the trunk of a car, crash the car, and SHOOT HIM NINE TIMES WITH A DESERT EAGLE .50 first. Also, he'll be cursing you out the whole time.
