He once killed a cougar. In a knife fight. note He had the knife, not the cougar. Although, it wouldn't be out of character for him to teach one how to fight with a knife. And then kill it.
"Theodore Rex" tells more: "Last Winter, in Colorado, he had leaped off his horse into a pack of hounds, kicked them aside, and knifed a cougar to death. What a great fight that had been!"
His boat was stolen once; he built another boat and hunted the thieves down. Instead of shooting them in the middle of the woods, he hauled them to town for court, going for 40 hours without sleep. He read Tolstoy to keep himself awake. When he finished reading Tolstoy, Roosevelt literally forced one of the robbers to lend him a book that he had been carrying. The guy who'd tried to get away with robbing TR was now forced to "volunteer" his book for his intended victim's reading leisure. This—on top of arresting him—means that Teddy completely and utterly humiliated the robbers.
After he received letters from army cavalrymen complaining about having to ride 25 miles a day for training, in response, Teddy rode horseback for 100 miles, from sunrise to sunset, at 51 years old, effectively rescinding anyone's right to complain about anything, ever again.
During his time in the badlands he once walked into a hotel when a drunken cowboy was shooting up the bar-room with a pair of revolvers. The drunk noticed him, called him "Four eyes", and said that "Four eyes is going to treat." Theodore ignored him and sat down at the bar, but the drunk came over to him, gun in each hand, and repeated his command. Theodore then said "Well, if I've got to, I've got to," and KO'd the drunk in three punches.
Awesomeness by Analysis: as an experienced hunter and military man, he fully understood alcohol will ruin a shooter's accuracy, and also that holding two guns even as your hands tremble from drunkenness is even worse.
Roosevelt's book Wilderness Hunter contained one of the first accounts of Bigfoot, Sasquatch and Yeti folklore in American letters. Teddy didn't see the big guy, but he'd heard stories.
Before he became president, while he was away on a hunting trip, someone hired a man named Paddock to either scare him off his land or just shoot him off it. When Teddy came back and found out that Paddock had been hired to kill him, he personally went to Paddock's house and told him "I understand you have threatened to kill me on sight. I have come over to see when you want to begin the killing.” Obviously, the threats ended then and there.
During his time as the head of New York City Police Commissioners in 1894, at a time when the NYPD was at its most corrupt. He more or less singlehandedly ended much of the political and criminal corruption in the NYPD and issued many new reforms, such as giving NYPD officers firearms, had telephones installed in station houses, made officers take regular firearms and fitness exams and hired more than 1,200 officers based on their qualifications, not their political connections. He even got a reputation for walking around the city late at night and in the early morning walking the beat of patrol officers to catch the ones who were nodding off and keep the rest on their toes. In summation: Theodore Roosevelt was a real-life Commissioner Gordon.
Another moment of awesome involved both Teddy and an enterprising gun designer. Said designer had made an effective compact shotgun utilizing a unique pump action that made it both reliable and compact, two qualities ideal for police use. How did he pitch his idea for Teddy? Simple: he booked an appointment with Roosevelt, shook his hand...then whipped out the shotgun, extended it, and fired five blank rounds in the air-all within the span of ten seconds. Roosevelt, rather than being pissed, ordered 100 guns on the spot.
During the Spanish-American War, he led a charge against an enemy position on San Juan Hill, showing way more calmness about being shot at than any man should. Especially since he was the only man on horseback, making him by far the most conspicuous target in the American ranks. After he reached the top, he proceeded to draw his revolver and kill an enemy gunner, clearing the way for his men and eventually getting him a Medal of Honor. When you are charging alongside John J. Pershing (who himself earned the Silver Star!) and you make people even forget "Black Jack" was there, You. Are. Bad. Ass.
Coupled with this, Roosevelt is the only man in history to earn both the Medal of Honor and the Nobel Peace Prize, a Violation of Common Sense if ever there was one.
Teddy loved to box, but he was blinded in one eye when he was sparring in the White House. So he picked up Judo instead.
Thomas Marshall said of his death, "Death had to take him sleeping for if Roosevelt had been awake, there would've been a fight." When people make analogies about fist fighting Death, it's safe to say you're the more most badass person on the planet.