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.
In The Familiar of Zero, Louise and the other nobles constantly say they are willing to give their lives to defend their kingdom, and will go on a Suicide Mission if commanded to by royalty. Saito constantly calls them out on how stupid this is. During Saito's Heroic Sacrifice in the season 2 finale (don't worry, he gets better) he fights not to die, but to live and see Louise and the others again.
Eren from Attack on Titan is this, contrary to what his allies think of him. When he fights, he has no time to let the prospect of death get in his way. He has every intention of walking out of each fight alive and frequently encourages this in others, especially in face of cowardice, apathy or doubt.
Eren: "If you win, you live. If you lose, you die. If you don't fight, you can't win!"
In A Certain Magical Index, Terra of the Left is unafraid of dying because he's completely confident that he will go to Heaven, despite his incredibly depraved actions. As Terra's dying, Acqua of the Back tells him he will obviously go to Hell for his sins, and Terra finally loses his smugness.
In All Fall Down: With her last words, Siphon proves she is this.
In one Chick Tract, a man encounters a burglar in his home and is disconcertingly delighted that he will be murdered, because he's lived a good life and is assured a place in heaven, so he's got everything to gain by getting there early. A bit of an Family-Unfriendly Aesop there.
In The Boy With The Magic Notebook, Battery doesn't care about Cauldron's hold over her anymore after Assault was killed by the Slaughterhouse 9. Yet they actually planned for this to have her do something different then in the original story canon...
In Predators, at one point mass murdering Serial Killer Stans catches Scary Black Man Mombasa by surprise and holds a knife to Mombasa's throat, demanding one of his guns. Mombasa calmly draws his pistol, puts it to Stans' head, and says that he 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.
In The Dark Knight Rises, Bruce isn't afraid of dying either, and that is the reason he can't escape the prison pit the first two times he tries. He eventually escapes by harnessing his fear of dying in the pit, helpless to save Gotham and climbs out without the safety rope, his fear spurring him to succeed.
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.
Parodied in Monty Python and the Holy Grail; Sir Robin's minstrel claims that Robin isn't afraid to die, but he very clearly is. Probably doesn't help that the minstrel keeps going on about the horrible things that could happen.
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. By the end of A Dance with Dragons Theon Greyjoy, someone who in earlier books was desperately afraid of dying, states that death holds no fear for him because it's honestly better than what his life is now.
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.
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. This is why Harry is the true "Master of Death". He does not fear it.
Achimas Welde, the Implacable ManProfessional 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.
Galaxy of Fear has its protagonists gradually become much more stoic about facing death - they don't like it and they strive to not be killed, they are afraid, but they aren't particularly upset. In Ghost of the Jedi, after Tash's brother and uncle appear to die, Tash debates with herself, and then decides to go after what 'killed' them anyway. She's sure that they and her parents will be there, if she dies, and the thought causes some degree of Dissonant Serenity - which is a good state to be in if one is using The Force.
Musashi, being about Japanese swordsmen, has a lot of this. One warrior temple actually has challengers sign a disclaimer. Musashi himself, although not particularly afraid of death, doesn't think too highly about samurai who brag about how much they don't fear it. They can die their heroic deaths if they want, as far as he's concerned, the only thing he'll settle for is heroic victory.
Parodied several times in Discworld. In Interesting Times, Cohen meets a soldier who is ready to die for his Emperor. Cohen kills him, and asks if anyone else is also willing.
One piece of advice General Tacticus gives in his memoirs is to welcome an enemy willing to die for his cause, as it means both of you have the same goal in mind.
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 threatening 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 villain 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.
In the Angel episode "I've Got You Under My Skin" the Ethros demon tells Angel that he does not fear dying at Angel's hands. The only thing he has ever feared is the horrible emptiness within his soulless former host.
"I find it amazing that you think that threats still mean anything to me. 'Do this or you're a dead man.' Death! Been there, done that."
Standard for heroes in the Stargate Verse. Everyone volunteers for every suicide mission, everyone is willing to put their life on the line when the occasion calls for it.
One of the spoken word fragments on Pink Floyd's The Dark Side of the Moon (just as "The Great Gig In The Sky" starts) is Abbey Road doorman Gerry O'Driscoll admitting that he is not afraid to die.
Gerry O'Driscoll: 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.
"Ain't Afraid to Die" by Dir En Grey. Lampshaded during the outro, when vocalist Kyo abruptly stops singing the final lines of the song, implying that he died before he could finish.
Robbie Williams' essay on self-loathing Come Undone contains the line "I'm not afraid of dying, I just don't want to."
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...
The title character of Julius Caesar is not afraid of dying even in light of all the ominous omens taking place in Rome throughout the night, telling those who try to counsel him not to go to the Senate that death "will come when it will come." But he is pretty bummed to find out that Brutus was among the conspirators against his life.
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 that 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, whose organization is based on the principle that they are willing to sacrifice their lives to defeat the Darkspawn. Furthermore, after they undergo the Joining ritual, their members have about thirty years left to live until they suffer ghoulification, whereupon they embark on their Calling, intending to end their days in the Deep Roads by performing a Last Stand against the horde, taking down as many as possible before they're finally slain.
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.
Commander Shepard often displays this in Mass Effect 2 and Mass Effect 3. Makes sense, since they've already done that, having been killed at the start of the second game.
Garrus: The Collectors already killed you once and all it did was piss you off...
However, by Mass Effect 3 various dialogue options suggest that Commander Shepard has become a borderline Death Seeker, putting it in a grimmer light. While Shepard is not actively trying to kill themselves, they are emotionally exhausted and EDI mentions their armour records them as being under more stress in their normal resting state than during the Skyllian Blitz/Battle of Torfan/Thresher Maw attack.
Mass Effect 3 also has Shepard's new shuttle pilot, Steve Cortez. Like Shepard, he's not actively trying to kill himself, but his husband's death during the events of the previous game wiped out his self-preservation instinct. Steve's survival depends on Shepard helping him get over this.
Yeul in Final Fantasy XIII-2. Which makes Caius' centuries-long Xanatos Gambit to "save her" somewhat unnecessary—too bad he doesn't realize it until the end. Also, Serah by the end: when Caius tries to unnerve her by saying she'll die if she continues on her path, she says she doesn't care anymore, and that if the future is saved, she's not afraid to die.
Ulthane from Darksiders. At one point War points a gun in his direction. Unimpressed, Ulthane simply shoves his face right into the muzzle.
Ulthane: Do I look like I'm afraid of death, Horseman?
In the Final Battle of WarcraftIII, Malfurion Stormrage comes up with a plan to defeat Archimonde by blowing up the World Tree right in his face. When Tyrande points out that this will rob the Night Elves of their immortality, Malfurion replies that if fear of death is enough to make them hesitate then maybe they have lived long enough.
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.
In RWBY, Ruby Rose is described this way. She is a great warrior, but very naive and idealistic, so she is completely nonchalant about death.