Vampire Killer and Other Whips
For a while the history of the Vampire Killer was rather muddy. As the primary weapon of Simon Belmont in the first Castlevania, the whip was certainly iconic even if its use didn't make a whole lot of sense. While vampire hunters in stories (like Dracula) had traditionally used stakes, garlic, holly water, and occasionally swords (for a good beheading), whips were not traditionally known for their vampire killing ability.
In our heads, we at the Inverted Dungeon tend to think a vampire would say (to paraphrase Austin Powers), "who uses a whip? Really?!"
The weapon had style, though, so it stuck around as the primary weapon for a whole host of heroes, only supplemented (via sub-weapons) with the cross, holy water, and other items to aid with whip wielders. Heck, even when a character was introduced that used a different weapon (like Eric Lecard and his spear) there was still going to be a whip-wielder by his side because that's how this series worked. It would take giving Alucard in Symphony of the Night to upend that dynamic (and that was only because the whip-wielder, Richter Belmont had take his whip with him when he seemingly went bad.
Even now, all these games later, people still associate Castlevania with dudes (and sometimes ladies) in leathers skirts fighting vampire with a whip. There's a reason that even the Castlevania-but-not series Bloodstained features a whip-wielder, Miriam going up against the forces of evil and the damned. That's just how you fight them now. In our collective consciousness, using a whip to fight evil just makes sense now.
About the Vampire Killer:
History of the Whip
Although the story of the Vampire Killer whip was initially muddled (we seem to recall the Castlevania III instruction manual saying that Trevor Belmont gained his powers via a blessing from the Poltergeist King, a character never mentioned in the series since), the history was eventually illuminated in Lament of Innocence.
In Lament, Leon, a warrior just back from the Crusades, has to travel to the castle of an evil vampire, Walter Bernhard, to save his kidnapped love, Sara Trantoul. While on the way, he encounters am alchemist, Rinaldo Gandolfi, who gave Leon a whip with the power to fight vampires, the Whip of Alchemy. Although the whip was capable of being upgraded over time, it wasn't near the end-game the whip's true potential was unlocked. Sara, who had just been bitten by the evil vampire, was rescued by Leon. Because of the bite, though, the poor woman was going to die. Instead she sacrificed her life so that her soul could be fused into the alchemy of the whip, making it more powerful (and able to damage master vampires and other demons).
Newly empowered whip in hand, Leon went on the defeat both Walter and Death (the whip was that powerful). It was then passed down through the ages, from Belmont to Belmont, to be used against whatever evil may appear. And, usually, that evil was Dracula.
This went on until just after the reign of Richter Belmont, blue-bedecked vampire hunter extraordinare). Soon after Richter's time using the whip, the Belmont family seemingly disappears. In their stead, a select handful of protectors for the whip step forward, most notably the Morris family (Quincey, John, and Johnathan). Together, they defended the land against Dracula and the forces of darkness, right up until the time of Dracula's last great defeat.
In 1999, a Belmont once again stepped forward to reclaim the whip. That man, Julius, took the whip to Dracula's castle and sealed it (and himself) inside to weaken Dracula's power and keep the castle locked for 35 years in a solar eclipse. It was only in 2035 that the castle, Julius, and the whip appeared once more.
Currently, Julius is the last known wielder of the Vampire Killer in the Castlevania timeline.
Vampire Killer in Combat
Whipping the Basics
For much of its time in the series, the Vampire Killer had a well known set of functions. Simon, Trevor, and Christopher all started with a leather version of the whip, the weakest form of it at the outset of a game. From there, collecting special morning star upgrades, the whip would change into a chain whip (with a morning star end), and then a longer form of the chain whip (for better range). Character death was the only way to lose the whip as otherwise the powered-up form would continue with the character through the game.
Only Christopher has a different variation on this theme among the original three heroes. For him, the third version of the whip would throw fireballs from the tip. However, if he took any damage (in Castlevania Adventure, as well as hard mode of Castlevania Adventure II) or specific damage (in Castlevania Adventure II normal mode), his whip would downgrade.
In the first games for the NES and Game Boy, the only change to this formula was in Castlevania II, where Simon buys upgrades to his whip instead of finding morning star upgrades. The upgrade path in the game was from leather to thorn whip, chain whip, morning star, and then flame whip, each increasing the overall usefulness of the whip against the hordes of monsters the player faced.
Of course, Simon just had to be different any time he could. Thus, in Super Castlevania IV, Simon has gained the ability to not only whip forward, but in all eight cardinal directions (being the only Belmont to ever do this). Plus, he was able to attack his whip to certain hooks and swing back and forth with it, gaining increased maneuverability around levels.
Other heroes, like John Morris and Reinhardt Schneider, were able to upgrade their weapons, although John was able to put a super powered twist on it: he could upgrade the whip a fourth time (so long as he didn't take damage), gaining a powerful lighting whip that could do a ton of damage to enemies. He was also the last hero to be able to swing via his whip, letting him take alternate paths in some areas of Castlevania: Bloodlines.
Let's Get Wild
Richter was the first to truly break the mold, featuring a version of the whip that didn't upgrade. Instead, for him, the whip started off in its morning star form. Because Richter could perform "Item Crash" attacks, powerful blows using his equipped weapons, he could engulf his whip in flame for a powerful forward blow (so long as he didn't have any sub-weapons in his inventory).
And then we have Nathan Graves. Although in his game the whip he uses is the Hunter's Whip, most assume this is just a variant on the Vampire Killer (the game more or less treated it like the same whip). With upgrades (via the DSS System), Nathan could empower his whip, granting it not only fire and rose-filled thorns, but ice, lighting, and all the rest of the traditional Castlevania elements.
That doesn't even count some of the ship-like items that have appeared in the series, most notably the Whip Sword. This item functions like a whip but is a blade. It's very strange and, generally not all that strong in its various appearances.
And then we have the whips from other continuities. Gabriel Belmont (of the Lords of Shadow series) uses a very vampire-killer like weapon called the Combat Cross. His descendants then use other, similar versions, one of whip is, in fact, called the "Vampire Killer".
Miriam, of the Bloodstained series, uses a whip to fight demons. Her whip doesn't upgrade at all, but it is much longer than most variants of the Vampire Killer.
And if we want to go very far afield and look at all Metroidvania games, even Samus has gotten in on the whipping action, using her grapple beam to not only cling to surfaces and swing, but she was also able to us it to latch on and pull switches and enemies in Metroid Prime 3.