Uniqueness Value

I'm mortal now. In fact, I'm the only Three in the whole darn universe. So I gotta worry about protecting myself.

—Number Three, aka D'ana Biers in Battlestar Galactica "The Hub"

I am the culmination of one man's dream. This is not ego or vanity, but when Doctor Soong created me, he added to the substance of the universe. If, by your experiments, I am destroyed, something unique--something wonderful--will be lost. I cannot permit that. I must protect his dream."

—Data, to Bruce Maddox in Star Trek: The Next Generation "The Measure of a Man"

Humans value the useful, the aesthetically pleasing, and the rare—so it is not surprising that we have a deep fascination with characters, races, or objects that are unique. Be it an artifact from a bygone age, a creature that is the Last of His Kind, or the last knight of an ancient and honorable order. Basically, the more unique a person or object is, the more valuable and worth preserving they are. Friends will fight to protect him, enemies to destroy him, and some even to possess him. Underscoring this is the reverse, that anyone/thing who isn't unique is vastly more expendable.

Maybe this is why both characters, readers, and the author place so much sympathy and interest in these characters. Faceless Mooks may die by the dozens, but their boss who is The Last Atlantean Wizard will at least get an offer of surrender from the hero. No one cares about destroying robots or AI's... unless they happen to be the only robot who can feel emotion. Or say there's a race of goo-people who are all clones and part of a Hive Mind? Finding ways to toast them would become a TV-show.

Relatedly, these unique characters will not just be rare, but powerful. Usually "their kind" is already powerful (which may be why there aren't any more of them left), but being their last representative gives the character a power boost much like the Inverse Ninja Law, sort of an inverse of being a Super Prototype. Although a super prototype is also generally unique in some way compared to the production models, which die easily, so it could go either way.

It's worth noting that these characters are by no means less likely to die. After all, their demise will evoke such a poignant End of an Age nostalgia few authors can resist.

In Real Life, this is part of the reason people are motivated to protect Endangered Species.

Examples of Uniqueness Value include:

Comic Book

Superman started out this way and its common for superheroes to be unique in this fashion because if everybody was like them, they wouldn't be all that super. After decades of encountering other Kryptonians, he was Retconned back into being the last of his kind after Crisis on Infinite Earths for precisely this reason. Now, its back to being not so unique with 100,000 kryptonians on a new planet on the opposite side of Earth's orbit, another race (the Daxamites) who have the exact same powers, and probably dozens of other Flying Brick types who vary only a little from him.
- Don't worry, those extra Kryptonians are in the process of being killed off.
- And compared to the Daxamites, Superman is unique in shooting him not being a perfectly reasonable course of action.

Film

The Creature from the Black Lagoon is not just a perfect specimen of his species dating back to prehistoric times, but also the only one left. Which of course makes the scientists want to study him... something that gets all the more complicated when he starts killing them and blocking the exits. Despite his terrifying actions, he is represented as a lonely creature, kidnapping the Hot Scientist and dying in a rather tragic way. For a B monster movie, anyway.
Most viewers of Hellboy II must have felt at least a tug at their heart strings when Hellboy killed the plant elemental, the last of its kind.
The Last Unicorn is so very, very precious to all involved because she is the last of her kind. However, after freeing all the other unicorns she remains unique because she's the only one to have ever experienced (and will remember) human emotion.
Star Trek has Vulcan be destroyed, rendering Spock, along with the few thousands of surviving Vulcans, an Endangered Species. Although, interestingly, Spock himself is not unique.
- Spock is, however a half human, and Nimoy's Spock is the only member from the original continuity in this newly split-off alternate continuity universe. Both Spocks are pretty unique in addition to being one of a few remaining Vulcans.

Literature

A strange aversion in Harry Potter and the Deathly Hallows is worth mentioning: Voldemort has made his Horcruxes out of three of the relics of the Four Founders of Hogwarts, priceless objects over a thousand years old, imbued with powerful magic that is only hinted at. However, they are steadily eliminated one after another—well, gotta catch 'em all to save the world—but one thinks that someone would have reflected, What A Senseless Waste of priceless treasures. It helps that they are keeping alive Wizard-Hitler.
The Dark Nest Trilogy has the Kiliks, several castes of insectoids with a Hive Mind. Naturally, they are extremely disposable, particularly compared to the Joiners, people of other species who were more or less absorbed into that hive mind and retain some vestige of individuality. The Kiliks regard themselves that way, since it doesn't matter for them if individuals get lost as long as the hive lives on. A Jedi Joiner shares their opinion; she works with a succession of members of the caste that relays communication best and is extremely fragile. Many of this caste get killed under her, all of them referred to by the caste name, and her reaction is always "Damn it. When does the next one get here?"

Live Action TV

Once Cylons in Battlestar Galactica lost the ability to resurrect, killing them got a lot more meaningful. Also, the Final Five (and Three after she was unboxed, as the page quote shows) are individuals, designed most of the Cylon tech, and know the way to Earth, making them some of the most unique and valuable people in existence.
Taelons in Earth: Final Conflict have been unable to reproduce biologically for centuries now, and had their homeworld destroyed by the Jaridians, making the death of any Taelon a heavy blow for them as a species.
The Doctor is the last Time Lord (Sometimes). Oddly enough the Doctor is probably the least powerful of his race, as he uses a TARDIS that was old when he will first steal it a few hundred years ago, and a few other assorted trinkets. Considering the Time Lords provide the page quote for Abusing the Kardashev Scale For Fun and Profit, he's positively roughing it. He's probably smarter than the rest of his people though, and he was already unique by being willing to do something about all the evil in the universe, rather than just watch.
There's usually at least one character like this in the main cast of each Star Trek series:
- As per the Page Quote, Data on The Next Generation. While he does find a handful of other robots like him, such as his Evil Twin Lore, they tend to get destroyed or are otherwise incapacitated so that by the end of the day, there's only one left.
- For Star Trek Voyager, There are two characters who fit this: Seven of Nine, for a while the sole Liberated Borg, who gets specifically chased down by the Borg Queen because of her uniqueness, and the Doctor, the only hologram who develops his own unique personality. It's little wonder they became the Spotlight-Stealing Squad.
- To some extent, also explored with Odo and Spock.

Western Animation

Storm Hawks has one episode devoted to helping a clutch of dragon hatchlings from being killed/captured by pirates, after dragons had been made all but extinct.
On at least one occasion, Superman has been abducted by a collector of endangered species for being the Last of His Kind.
- Along with Lobo, who claims to be a self-made Last of His Kind.
Same deal for Danny in Danny Phantom where Skulker wanted to collect him because of his rare half ghost status. Though after numerous failures to capture him, Skulker decided to just kill and pelt him instead.
- Sam was kidnapped by an egotistical ghost prince who wanted the novelty of having a human for a wife. How to pick the right one for the job? Hold a beauty contest at the Ghost Boy's high school.
Parodied in an episode of The Simpsons when Marge and the Pre-Teen Braves are surprised to meet a Mohican.

Bart: Mohican? I thought you guys were all gone.
Mohican: No, but we encourage the myth. Chicks really dig you when you're the last of something.

Video Games

Wander's goal in Shadow of the Colossus is to destroy all the colossi in order to resurrect Mono. However the more you play the game, the more you feel like destroying these ancient and unique creatures is too high a price to save one random girl. Especially those colossi who ignore you until provoked, or don't even fight back as you attack them; you end up feeling guilty every time you send another giant beast collapsing in slow motion.
- Another giant, beautifully and painstakingly crafted, intelligent (or at least sentient), emotional creature... usually letting out a horrible final moan or gasp as the lights fade from its eyes... excuse me a moment...
Explored in Planescape: Torment when you discuss the modron race with Grace. When a modron is destroyed, its essence returns to Mechanus, and a new modron of the same type is spawned. Since all modrons of a given type are identical, slaying one amount to nothing. However Nordom, a recruitable party member, has gone rogue and developed his own personality and individuality. If he is destroyed, his essence will also return to Mechanus, but the replacement will be a standard modron - not Nordom. The Nameless One even points it out - by going rogue, Nordom has effectively become mortal, since his death would be considered a loss. (This is, incidentally, why in the regular Planescape setting modrons make such a big deal out of hunting down rogue modrons - they are effectively stealing vital Mechanus essence for non-Mechanus purposes.)

Web Comics

In The Inexplicable Adventures of Bob, Molly is protected by the Endangered Species Act because she's the only one of her species in existence. Since Galatea's birth, there are actually two, three, counting the giant baby Voluptua took away, but that still ain't very many.
In The Wotch, the Unicarn demon is the last of it's kind, because as a child, it wiped out the rest of its people. As a child. When he grew up, he REALLY started to regret that...

Real Life

Fortunately, this is why we're so big on protecting endangered species. Tragically, this is why it's hard to get anyone worked up about a species being over-hunted until there's only a few left.
The two primary aspects of value are spacial and chronological rarity: how much of something there is, and its longevity. While one might argue that these are only relevant in the context of a thing's utility, that rarely comes into play. It is effectively guaranteed that if something is (or perceived to be) distinct, unique and fragile / short-lived, that humans will covet it eagerly... even if it is completely useless and rather ugly.