Not Afraid to Die

Kazim: If you don't let go Dr. Jones, we'll both die!

Indiana Jones: Then we'll die!

Kazim: My soul is prepared! How's yours?

—Indiana Jones and The Last Crusade

For whatever reason, whether it's because of everything they've experienced or lived through, this character lives without any fear of death. They don't actively look for it the way the Death Seeker does, but if it ever comes for them, they will face it graciously, without crying, whimpering, or trying to make a Deal With the Devil. They're going to face up to it.

A prime trait of any Badass, Blood Knight, and pretty much anyone who makes a famous Last Stand, Heroic Sacrifice, decides to Face Death With Dignity or with some Famous Last Words. Also a trademark of the Shell Shocked Veteran, and Old Soldier. When this character finally passes on, the will always have an Obi Wan Moment; sometimes it will be a Dying Moment of Awesome, as well. Doing this at the wrong time may result in a Stupid Sacrifice, however.

Compare Don't Fear the Reaper (which is about not fearing the personification of death, rather than death itself) and We All Die Someday (which is about the acceptance of your own mortality).

Examples:

Anime and Manga

Bleach: According to Kenpachi Zaraki, every Soul Reaper captain except Gin Ichimaru and Kaname Tousen. Yamamoto later affirms that it is part of the oath and duty of being a Gotei 13 captain to not be afraid to sacrifice one's life for the greater good.
In One Piece, this is a trademark of those with the "Will of D." (those with the middle initial D.). Other characters are baffled as to why they all Go Out With a Smile (including Luffy when he was almost executed by Buggy).
- Subverted, however, by Marshall D. Teach aka Blackbeard, who begs for his life as Whitebeard is about to smash his head open.
In Cowboy Bebop, one of Spike's character traits is how blasé he is about the prospect of dying. He states several times that he's already died and is just watching a bad dream until he's ready to wake up and face the reality that he's dead. Encountering Tongpu temporarily drives the cool away from him, but in all other instances (including in several episodes and The Movie that took place chronologically later) Spike never seems afraid of death. Depending on how you interpret the ending, the last minutes of the series shows the crowning example.

Comic Books

In All Fall Down: With her last words, Siphon proves she is this.

Film

As seen from the quote up top, both Indiana Jones and minor character Kazim from Indiana Jones and The Last Crusade count.
In Predators, at one point mass murdering Serial Killer Stans catches Scary Black Man Mombassa by surprise and holds a knife to Mombassa's throat, demanding one of his guns. Mombassa calmly draws his pistol, puts it Stans' head, and says that Mombassa isn't afraid to die, then asks if Stans can say the same. After a few seconds in a standoff, Stans backs down.
In The Last Samurai, Katsumoto identifies Algren as not being afraid to die, but sometimes wishing for it. By the end of the movie, Algren has started to lose his death wish. Being good Samurai that they are, Katsumoto and his men are already like this.
Half Past Dead: Lester, an inmate due to be executed for the accidental deaths of five federal agents in a Train Job gone wrong, is depicted as being bothered more by the waiting than by his impending death. He feels that he deserves the death penalty for what he caused.
Heavily subverted in X Men Origins Wolverine when Victor Creed, aka Sabretooth comes to assassinate his ex-team member Bolt. This little exchange takes place:

Bolt: I'm not afraid of you, Victor. I'm not afraid of dying.

Creed: How do you know? You've never tried it before.

The Joker in The Dark Knight doesn't even seem to care about the prospect of his death. In fact, it's almost what he's hoping to happen. He would love nothing more than for Batman to kill him to prove that in the end, everyone is just as monstrous as he is.
Subverted (maybe parodied) in If Looks Could Kill:

Michael Corben:I am not afraid to die. I am not afraid to die. Who am I kidding?

In Kingdom of Heaven the hospitaller is told he will certainly die if he goes with the army. He replies, "All death is certain" and rides away.

Literature

Any number of soldiers and badasses from A Song of Ice and Fire ranging from the honorable to a fault Eddard Stark to amoral badass Jaime Lannister.
Henry Istelyn in The Bishop's Heir, about to be hanged, drawn and quartered, his eyes "meeting the archbishop's frigid glare with a serenity and even compassion which made Loris drop the contact first, to gesture brusquely to the guards." The guards are also put off-balance when Istelyn stubs his toe on the scaffold steps and murmurs an apology.
In Harry Potter, those who aren't afraid to die can't become ghosts. This includes Sirus and Dumbledore.
- This trope is also the ultimate difference between Harry and Voldemort. While Voldy has done everything to keep himself alive, Harry accepts, in the end, that he'll have to die to make Voldemort killable.
Achimas Welde, the Implacable Man Professional Killer from Death of Achilles, is afraid of being crippled but not of pain or death. Ironically, he is crippled by Fandorin in the end of the book... and so he chooses to bleed out and die instead of accepting Fandorin's help.

Live Action TV

Invoked in Burn Notice. In one episode, Michael is pretending to be a dirty security guard who's going to help on a heist. The Villain of the Week is theatening to kill Michael if he doesn't help; Michael goes along with this because that's what he wants, as he intends to ensnare the villain in a trap. However, something happens that changes the situation, and Michael needs to have the heist called off. Michael, as the security guard, is pivotal to the heist, so he convinces the villain that the guilt he's feeling has caused him to have a Heel Faith Turn and that he is no longer afraid of dying. The ploy works; the villian realizes that you can't threaten to kill someone if they're not afraid of death, so he backs off.
Scrubs: In "My Old Lady", Mrs. Tanner quietly refuses dialysis, explaining that she has enjoyed her life and is ready to die. Later, it is shown that J.D. is much more afraid of death than she is, and she ends up comforting him.
In New Tricks Jack Halford admits to being one of these and explains it's the reason he tackled two armed criminals and why he doesn't want the commendation he's been awarded for it.
In The Comic Strip Presents: Oxford the gun-toting bad guy is confronted by a group of elderly professors who aren't afraid to die because they're all over 60.

Music

One of the spoken word fragments on Pink Floyd's The Dark Side of the Moon (just before The Great Gig In The Sky) is Abbey Road doorman Gerry O'Driscol admitting that he is not afraid to die.

Gerry O'Driscol: And I am not frightened of dying. Any time will do, I don't mind. Why should I be frightened of dying? There's no reason for it — you've all got to go sometime.

Stand Up Comedy

George Carlin once cited this trope as a reason that applying the death penalty to drug dealers was doomed to failure.

Drugs dealers aren't afraid to die. They're already killing each other on the streets, every day, by the hundreds! Drivebys, gang shootings, they're not afraid to die. The death penalty doesn't mean anything [as a deterrent] unless you use it on people that are afraid to die. Like the bankers who launder the drug money...

Video Games

Wynne from Dragon Age: Origins has in fact already died, but was kept back by a benevolent Spirit of the Faith entering her body and using its own power to keep her alive. However the strain of this is weakening the Spirit, leading her to realize she can collapse and die at any moment. Nonetheless, she is perfectly fine with this because she has no regrets about the life she lived (except one, which you can help resolve in her personal sidequest), devoting her remaining time to aiding the Warden.
- This is brought to the point in the supplementary novel Asunder, where Wynne, without batting an eye, transfers the spirit has has kept her alive for eight years to the fallen Templar Evangeline, resurrecting her but dying herself.
- This is also embodied by the Grey Wardens, who's organization is based on the principle that they are willing to sacrifice their lives to defeat the Darkspawn, have only 30 left years to live after Joining and will end their days by entering the Deep Roads to perform a Last Stand against the horde.

"In War, Victory. In Peace, Vigilance. In Death, Sacrifice."

Jak X: Combat Racing: Poisoned, receiving death threats and a bounty on his head, Jak states that he's not bothered by any it and that he's not afraid to die. Daxter on the other hand...

Daxter: Whoa! Freeze frame! I'd like to go on record right here that I'm firmly and officially against dying. In any way.

Visual Novels

Shiki Tohno, the protagonist of Tsukihime, has very frail health and is perfectly at peace with the fact that any moment, his life can cease for no particular reason.
- It helps that he literally sees death everywhere (without his glasses) and has actually been killed before. Though he's not dead either. It's a little weird.

Web Comics

Ellen in El Goonish Shive was like this while she thought she was going to exist only until the end of the month.
In The Mansion of E, Crud the Gnoll displays this attitude at one point