Tallahasse, from Zombieland, whose picture formerly graced the main page. While Columbus, is simply trying to survive, Tallahassee, deals with his depression brought on by the apocalypse by eating Twinkies, which he can almost never find. And he is so awesome that sometimes he is forced to rely on improvised weapons. At the climax, he's using rollercoasters.
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..
Lord Cutler Beckett:You're mad!note Jack is attempting to escape from Lord Beckett's ship in At World's End by blasting its mast down with a cannon and riding its rigging back to the Black Pearl.
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.
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 off 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 re-imagining of The Wolfman 2010. He's essentially a very British gentleman explorer, except old and really, really crazy.
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.
Secondhand Lions: "Near as I can figure, they were trying to fly the plane upside down through the barn."
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?
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.
Eastern literature proficiency bonus: Read The Journey West. Rewatch Thirteen Assassins. Yup, exactly.
John 'Bluto' Blutarsky from "National Lampoon's Animal House", speaking of Belushi - Wild Bill Kelso in '1941' also counts.
As with Jim Carrey pretty much any character he played had at least a touch of this.
Ashley J. 'Ash' Williams from the Evil Dead franchise is the living embodiment of this trope, and not just because he's played by Bruce Campbell. We are talking about a guy who arguably had the worst week of his life, what with having his friends, sister, and girlfriend demonically possessed, forcing him to kill them, and then when he thinks his managed to escape the nightmare, he still gets possessed by the evil force, and that's only day one! He still manages to continually throw off demonic influences (and cuts off his own hand with a chainsaw after it tried to kill him), survived another night that the new arrivals at the cabin didn't, and then proceeded to get sucked into the past to stop an army of the undead from conquering the world... Okay, so, yeah, he is the reason the army was raised in the first place, but he still managed to kick their collective ass with the help of his new buddies, some science text books and his redesigned car, The Deathcoaster.
Doc Brown in Back to the Future. He builds all manner of gadgets but his Crowning Moment of Awesome would be a time machine. Built out of a DeLorean because he wanted to do it with style. To get it up to the eighty eight miles an hour to time travel is almost as impossible as time travel. The idea to make it possible came after he hit his head on a toilet seat. He gets the uranium needed for it to work by ripping off Libyan terrorists with a pinball machine. On its test he has himself and Marty stand right in the car's path believing the car would go through time rather than run them over. In the past he slides down an electric cable from the clock tower and electrocutes himself to get the time machine to work. When he is accidently sent to the Old West he has Western Union deliver a letter to Marty at the exact time and place where the De Lorean malfunctioned, sixty years later. He built a giant Steampunk machine to make ice cubes and a sniper rifle out of a telescope. And at the end after swearing off time travel he builds another time machine, built out of a flying locomotive, with his children Jules and Verne and his wife from a hundred years ago. That should do it.