The Force Is Strong with This One

"Darth Vader: "He is here."

Grand Moff Tarkin: "Obi-Wan Kenobi? What makes you think so?"

Darth Vader: "A tremor in the Force. The last time I felt it was in the presence of my old master.""

- Star Wars: A New Hope

Suppose magic, ki, or Psychic Powers exist, and that there are people who possess these powers. Naturally, how strong a given person is with these abilities will be a big factor in the plot, both in the ass kicking scale and in terms of how characters act and react to each other. But how can writers convey that to viewers? Sure, generally the rule is "show, don't tell", but what if a given character's psychic powers are to pinch shut the carotid artery? Or their Supernatural Martial Arts can crack a planet in two? Having them remind viewers "Luckily, My Powers Will Protect Me" gets old fast. And you can't very well have them show the power off every time they appear so new viewers can get clued in, just imagine what that'd do to the Special Effects budget!

So instead writers will give these characters the secondary (or primary) ability to sense each other's power, much like internal Stat-O-Vision that is represented with conveniently color coded Aura Vision. Typically, The Empath or someone with a Significance Sense or Spider Sense will be able to tell the raw Power Level of an opponent, what brand of magic they use (especially if they're evil) and the like. Expect them to intone, "The Force is strong with this one," or a variation when a powerful enemy draws near; especially common is for the sensor to intone "Such oppressive evil power!" before fainting or falling to his knees in fear.

This can result in one being a Weirdness Magnet.

It's practically a requirement for any Shonen Anime or Manga that at least one person can do this (often a Mentor and someone else in the hero's group to take over when the Mentor Occupational Hazard kicks in), especially right before a climactic battle. Western media may use Cower Power, a Game Face or other methods to show this off.

The Trope Namer is Star Wars: A New Hope.

Anime & Manga

 * Elfen Lied of all things has this; Diclonii can sense each other's presence out to a certain undisclosed range, accurately enough to positively ID the other diclonius through this sense alone if they've met in person before.
 * It actually makes sense if you consider Nyu a depowered state of Lucy.
 * In the manga, the Unknown Man takes advantage of this in the most horrific way possible.
 * In Bleach, Soul Reapers (and other spirit creatures such as Hollows) can detect the level of spiritual pressure (Power Level) another creature has.
 * Dragon Ball Z. Lots of times. Notably, all the races affiliated with Freeza did not know of this ability or how to use it, and instead relied on mechanical devices. Once the Power Level numbers started getting out of hand, the series went back to using this full-time. This actually proved to be a drawback in the Android Saga, since the mechanical / cyborg villains were undetectable.
 * Gundam has Newtypes who have this ability.
 * Saki is a manga about Mahjong, and therefore, strong enough mahjong players can feel the auras of other strong mahjong players.
 * In one chapter of the spin-off Saki: Achiga-hen, the main characters (a different group of girls) pass Saki in a hallway at the competition venue. Their coach (said to have been the strongest player in the history of their school) and one of their most skilled players freeze up in terror as she gets closer, despite not even knowing who she is. The rest of the main characters, including Shizuno, have no idea what's going on...then Shizuno, despite being the worst player on the team, feels a chill run down her spine when Saki passes right by her.
 * Soul Eater gives this ability to anyone who has "soul perception" (and can thus see the souls of living people). This is shown the viewer via a Color Coded for Your Convenience (blue = good, red =bad, purple = witch or misc.) glowing ball of proportional size to their power (with "accessories" for different characters).
 * The colour coding is anime-only, perhaps because it specifies 'evil' human souls (hence red = bad) whereas the manga does not.
 * There are also degrees of soul perception. Some, like Stein, can pick up on individual characteristics and emotions, others can sense when people are lying and see through the soul protection skill of witches (BJ), or extend their 'sight' over large distances (Azusa's clairvoyance). Maka can detect souls over wide areas (though not to Azusa's level...yet), picks up on emotions, and is implied (the Baba Yaga arc might have confirmed it?) to be good enough to see through Soul Protect.
 * Maka frequently comments on the soul of whoever she is fighting, and Gopher for one is not impressed with her "peeping". The one time she was shocked with the results was early on when she sensed a true witch's soul for the first time. Considering it was Medusa, she had every reason to be scared.
 * In Fullmetal Alchemist, the Xingese characters can feel the flow of the planet's natural energy, which is useful for finding homunculi, who feel like several dozen people in one body.
 * Various characters, usually with the help of Millennium Items, in Yu-Gi-Oh!.
 * Judai gains this power in Season 4 of Yu-Gi-Oh! GX. His spirit partner Winged Kuriboh seems to possess it from the beginning.
 * Most ninjas in Naruto can feel the chakra of others while fighting them up close, but the ability to detect and gauge it from a distance is very rare. Karin, Fu, Ao, and C are some examples. Karin has also shown to use it to become a Living Lie Detector and can hide her chakra from other sensors (but can't sense herself when doing this), but it's unknown if anyone else can.
 * Sage Mode also grants it's user the ability to sense chakra from a distance, likely because the power involves controlling the natural chakra around him.
 * Kisame's Samehada can apparently sense/smell especially large bodies of chakra. This is possibly a reference to shark's ability to find prey with electrolocation.
 * Later when Naruto enters his new kyuubi form, he can sense negative emotions, thanks to nine-tails.
 * The Hyuuga clan with their Byakugan can do this see chakra.
 * Akamaru can smell chakra.
 * Some members of the Yamanaka clan can do this.
 * Pain could detect a person's strength if it stepped into "his" rain.
 * In Full Metal Panic, a variation of this can be found with Sousuke. He's shown to have a sort of sixth sense, in that he actually has the ability to sense "killing intent" in the air, and can somehow know when there are enemies that want to kill him. He demonstrates this ability several times, though one of the more pronounced instances can be found in the later novels. Tired, wounded (having had ), and confined to a hospital bed, he was shown to be able to sense a bunch of soldiers sent to kill him, and therefore managed to lay a trap for them by the time they arrived.
 * Apparently, it only works for when people are out to kill him specifically. If this worked on people trying to kill someone else,the show wouldn't have most of its comedy.
 * The fact that he's extremely paranoid ( for good reason, due to his history) probably helps.
 * In Code Geass, it appears that those who possess a Geass Code or are in the Sword of Akasha can sense Geass users.

Fanfic
Dreaming of Sunshine features Shikako, who is a chakra sensor to the point that she can see through disguise jutsu of people she knows well, gauge and enemie's aproximate strength, and detect lies.

Film

 * Star Wars. Vader names the trope when he's chasing Luke down the Death Star's trench, and finding himself unable to get a solid lock. Vader also senses Obi-Wan's presence aboard the Death Star.
 * Decades earlier, Qui-Gon had sensed Anakin's potential.
 * In Revenge of the Sith, Palpatine quotes this line when he dubs Anakin "Lord Vader" for the first time.
 * The third X-Men movie had a mutant who's only ability was to detect other mutants and ascertain their relative "power-levels" on a 1-5 scale. Only one level 5 has ever existed, and when she tells Magneto that she just became aware of a "level 5", he immediately knows that she refers to Jean Grey's "Phoenix" personality.

Literature

 * Female channelers in The Wheel of Time can always sense the strength of fellow female channelers, and perceive a glow around females actively using magic. All channelers can sense their own gender's magic in use, and spells are possible to sense the other gender's. Males channelers get goosebumps when females close by are using magic. There are also techniques to hide both ability and active use.
 * Lampshaded by Tyria Sarkin in Wraith Squadron. She once says of herself, "The Force is weak in this one." She's Force-Sensitive, the last of the Antarian Rangers from Toprawa, but her Force powers are weak, and she feels overwhelmed by what she has to live up to.
 * Wizards in Septimus Heap can feel somebody's else's Magykal powers, which makes Marcia feel Septimus's Magyk long before he's revealed. Jenna feels his Magyk too in the first book.

Tabletop RPGs

 * Vampire: The Requiem has Blood Potency and The Beast. The higher a vampire's blood potency, the more blood they can store and spend, and the harder they are to affect with negative powers. As BP rises, The Beast gets stronger too, so every time a pair of vampires meet, their Beasts will "confront" each other, with the stronger of the two trying to incite an Unstoppable Rage in its host, and the weaker one to make its own run away screaming.
 * Promethean: The Created has a similar rule -- "Azoth [the "Divine Fire" that gives Prometheans life] calls to Azoth." On the plus side, whenever two Prometheans are within a certain distance, they can feel their Azoth tugging towards each other. On the minus side, so can the Pandorans...
 * The Detect advantage in GURPS is this in a nutshell
 * AD&D has spell Wizard Sight, used to discern arcane and divine casters and appraise spellcasting potential, and see magical auras of objects instantly and certainly (unlike "detect magic" probe).

Videogames

 * Keyblade users in Kingdom Hearts can sense light and darkness of peoples hearts as well as sense the hearts of people familiar to them. Only Terra and Aqua make use of this regularly however as it requires quite a bit of training. Since Sora hasn't gotten official training he's only made use of it once so far.
 * Lufia seires's Spiritual Force, which both heroes and big bads lampshade whenever they meet. By the DS remake, detection and unleash of Spiritual Force can be done even by oldmen.

Webcomics

 * Sensei Greg in El Goonish Shive feels active magical forces (including shapeshifting) around. discerns the magical potential in people.

Web Originals

 * Boris "The Bloodhound" Lydecker from the Global Guardians PBEM Universe is a reporter for Capes and Cowls magazine (imagine Us Magazine if it concentrated on metahumans rather than celebrities). He is, himself, a metahuman with the sole power to detect other metahumans, including he general nature of their powers and power level (along the lines of "something to do with fire... but wow does he have a lot of it"). His usual assignment is to "out" superheroes who haven't revealed their real names to the public yet. Naturally, he's not well liked in the superhero community.
 * Mentalists in the GGU can always sense other mentalists whenever they get into close proximity; ironically, it is the least powerful and least experiences telepaths who are sensed more strongly, because they have a harder time keeping their "psychic leak" as it is called, under control. Powerful telepaths, or very experienced yet only mildly powerful ones, only leak a little.
 * Wizards and other mystics in the Global Guardians PBEM Universe can automatically detect the presence of other wizards and mystics, but they can only detect each other's power level if the other mystic is either currently spellcasting or if they voluntarily "project their aura of power", thus intentionally advertising just how powerful they are.