Cigar Chomper

Because nothing says "manly" like a phallic symbol clenched between your teeth. Clockwise from top-left: Vice Admiral Smoker, "Hannibal" Smith, Sergeant Johnson, and Arnold Schwarzenegger

A character who is never seen without his cigar. Almost Always Male. Tends to denote that the character is a tough, aggressive, take-no-nonsense type. Because good cigars are an expensive habit, they also carry a connotation of wealth, power and high status. Characters such as Da Chief, Sergeant Rock and your local Corrupt Corporate Executive often chomp on cigars, as will anyone in a Smoky Gentlemen's Club who hasn't got a pipe.

Examples of Cigar Chomper include:

Anime and Manga

The title character of Space Adventure Cobra.
"Sir" Integra Hellsing is a female example.
One Piece: In general, while a lot of characters smoke, someone who smokes cigarettes is ally of the Straw Hats, while cigars indicate an enemy.
- Smoker/Chaser is usually seen with multiple cigars...unless it's the 4kids dub. Justified, of course, as his Devil Fruit power lets him manipulate and control cigar smoke in a variety of useful ways.
- Sir Crocodile, Shilew of the Rain and "Golden Lion" Shiki also smoke cigars. Also, all three are evil.
- Capone Bege from the Whole Cake Island Arc, works with his mobster-style suit and attitude.
Bunta from Initial D almost always has one.
Balalaika in Black Lagoon is an another female example.

Comic Books

Robot example - Kup is portrayed as this in IDW's Transformers comics, starting in All Hail Megatron. It's apparently called a "cy-gar".
- Its also medicinal, as it contains radiation that prevents him hallucinating zombies.
J. Jonah Jameson, the Mean Boss at The Daily Bugle where Spider-Man works in his civilian identity.
Nick Fury (before Joe Quesada decreed that no Marvel characters were permitted to smoke).
Ben Grimm, for the first thirty years or so.
Lenny Balinger, the foreman for Damage Control in the Marvel Universe.
The Comedian in Watchmen
Wolverine until the mid 90s or so.
Perry White in Superman ... sometimes. In one story he gave up after a lung cancer scare. That seems to be getting ignored now.
Detective Casey in Mickey Mouse comics subverts. He thinks he's tough and respected by both colleagues and crooks....
Lobo
Jonah Hex
Julius Furst, BFG-toting Badass Normal of Astro City.
Sam Hagen, Ryder's boss from the old The Creeper comics.
Hellboy is fond of cigars.

Film

The Man With No Name from A Fistful of Dollars.
Miracle on 34th Street: Charlie Halloran (played by William Frawley, Fred of I Love Lucy) as the Judge's campaign manager. He even chomps on it in court, although it's not lit.
Hellboy loves his cigars, and so does his boss. In fact, it's the one thing they have in common.
General Ripper from Doctor Strangelove is a parodically Freudian example.
The Mayor in Sucker Punch.
Sgt. Apone in Aliens.

Literature

In the novel To Kill a Mockingbird, this was Judge Taylor's "one interesting habit", as he was a pretty boring man otherwise.
LEP Commander Julius Root of Artemis Fowl.
Inspector Cramer in the Nero Wolfe novels, who almost never actually lights his cigar, just gnaws on it.
Commander Vimes in Discworld.
Invoked by Citizen Rear Admiral Lester Tourville in Honor Among Enemies. He smokes cigars as part of a general strategy of looking like a hard-charging cowboy and less like the sort of responsible officer who tends to get promoted to a high enough position in the Peoples' Navy to either be seen as a potential threat to the Committee Of Public Safety or to warrant their preferred punishment for Citizen Admirals who have failed in important missions.
Invoked in The Warrior's Apprentice. Baz apparently once served under a tough, cigar-smoking engineering officer. Miles successfully gets him to intimidate the Oseran engineers by giving him a cigar as a prop.
The goblin leader in Blue Moon Rising is a classic Cigar Chomper.
Sgt. Veelie, Inspector Queen's offsider in the Ellery Queen novels. Especially apparent in the 1970s TV series where Veelie (played by Tom Reese) is almost never seen without a cigar in his mouth.
Uncle Cyrus from "Anthill" has had numerous cigars.

Live Action TV

Hannibal from The A-Team.
Al from Quantum Leap.
Starbuck from the original Battlestar Galactica loves this trope -- and the Starbuck from ]the reimagined series is one of the rare female examples.
Columbo, though having a timid, obfuscatingly stupid thing going on, is never seen without a smelly cigar in his mouth.
The Dukes of Hazzard: Boss Hogg, the main antagonist.
The Burns and Allen Show: George Burns, who for most of his adult life was a cigar smoker.
All in The Family (and continuing through Archie Bunker's Place): Archie Bunker, the main protagonist.
Raoul, the Cuban exchange student who lives with the Petrovskys in the 1976 sitcom Ivan the Terrible.

Newspaper Comics

Flip from Little Nemo.
Albert Alligator from Pogo.
Broom Hilda was one of these initially, but this was eventually phased out due to concerns about promoting smoking to young readers.

Oral Tradition

In Brazilian folklore, the Caipora is a Trickster God who appears as a small man riding a hog, who smokes a cigar.

Video Games

Duke Nukem.
One of the official artists for Team Fortress 2 has done a series of unofficial genderbends of the main characters. Her design of Lady Heavy frequently has a cigar, a rare female example of this trope.
In StarCraft, the Firebats can always be seen smoking a cigar inside their armor.
- Tychus from SC2 has a few notable moments with cigars, although it's not constant. The still image of him used in all the promotional materials features one.
The Sly Cooper games give us Muggshot from the first game and El Jeffe from the fourth, who both are seen with a stogie locked in their jaws in their debut appearances.
Pyro from Sacrifice has a cigar as part of his character portrait and is thus never seen without it. He's more of a Corrupt Corporate Executive, however.
Mass Effect II: one sight gag in Omega is an elcor merchant who constantly smokes a cigar, somehow.
Left 4 Dead: Bill is an interesting case, being a cigarette chomper. He doesn't really smoke it, despite its constantly being lit, just kind of of keeps it there all day. It even stays lit after he dies. The only time it's unlit in-game is after he's been Killed Off for Real.
Halo: Sgt. Major Avery S. Johnson. The tough-as-nails smartass Johnson is hardly ever seen without his cigar.
Peacock from Skullgirls. Notable in that Peacock is a 13 year old girl.
Jinx from Jak and Daxter.

Web Comics

Manly Guys Doing Manly Things hangs a very nice lampshade on it in this strip.
The Beta Red manager in The Unspeakable Vault of Doom.

Web Original

Roman Torchwick from RWBY.

Western Animation

Warren T. Rat, the villain from An American Tail.
Carface from All Dogs Go to Heaven.
Pete from the Classic Disney Shorts.
Quite a few of the Gas House Gorillas (particularly the pitcher) in the Looney Tunes cartoon Baseball Bugs.
The Simpsons: Krusty the Clown.
Futurama: Bender
Rock Bottom from the Felix the Cat TV series

Real Life

Anything featuring Winston Churchill.
Arnold Schwarzenegger in Real Life. Note that Arnold is so devoted to his cigars that when he was Governor of California, it being illegal to smoke inside office buildings, he had a tent with his desk placed on the grounds outside the Governor's Mansion so he could smoke while conducting business.
British TV executive Lew Grade. A producer working for him once allegedly complained that his salary was less than Grade's cigar budget. Grade replied that the producer didn't give him as much satisfaction as his cigars.
Fidel Castro, who certainly liked to be seen as a tough military leader.
Che Guevara is quoted as saying, "A smoke in times of rest is a great companion to the solitary soldier." Unfortunately for him, he also had terrible asthma, which became a liability during his disasterous Bolivian campaign.
Clive Barker's cigars got bigger as he got more rich and famous.
Groucho Marx. Not physically tough, but woe betide anyone who dared spar with him verbally.