Supernatural Sensitivity

In any setting where there are people with uncommon powers, be they magical, psychic or ki-based, it's a common trait for those blessed with such abilities to be able to sense it in others. This often results in simply having characters remark of one another: The Force Is Strong with This One. But sometimes, they sense more than the sheer amount of power and can actually detect fine details in what's going on. There are two basic ways this works:

Activity Detection
Characters can sense when others are using magic, and perhaps exactly what they're doing. Often tied to vision or hearing, but could also just be some sixth sense unrelated to those possessed of normal people. The signs of magical use are diminished over distance, and by the degree of power being emitted. There are probably tricks to avoid detection or dampen the signs of use, and other tricks to see through those.

Residual Detection
Use of magic leaves signs which can be sensed by those with the right gift. Any place where magic has been performed, and any object or person under the effect of a spell will have a residue that fades with time. The amount of detail which can be gleaned from this method varies. This is common in settings which have a Background Magic Field.

The sensitivity of magic-users to one another is important in the development of a magic system. It acts as a limiter on the more powerful users in High Fantasy: The mighty wizard could wipe his current foe off the map with ease, but doing so would attract the attention of much darker and stronger forces. Thus, he has to resort to more subtle and indirect magics, and save his strongest stuff for true emergencies. Sensitivity also plays a key role in unraveling a plot, as the characters check residues and enchantments to try and uncover who did what long after the fact.

Often tied to Aura Vision. See also The Empath, who may have these abilities, Psychic Radar and Detect Evil. Not to be confused with Super Senses.

Anime and Manga

 * Bleach. Powerful spirit creatures such as Soul Reapers and hollows can detect the use of spiritual pressure (spirit energy) a considerable distance away.
 * Detecting the aura of Youkai is a useful ability in Inuyasha, common to Youkai themselves, Hanyo like Inuyasha, and to ki using humans like Kagome and Miroku. Even exterminators like Sango could sense it to a lesser extent. In the Anime there was an old exorcist who was completely insensitive.
 * In Rosario + Vampire, Inner Moka teaches Tsukune how to do this in season two.
 * Kekkaishi have the ability to sense when an Ayakashi enters the Karasumori site.

Literature

 * Sorcery in The Belgariad and related works makes what is described as a "sound", which can be mistaken for mundane noise under some circumstances. The sound can be lessened by doing things slowly, and shapeshifting, because it's directed internally, is very quiet. The protagonists are often forced to avoid sorcery in enemy territory because of this noise effect. Interestingly, other forms of supernatural power, such as magic, wizardry, necromancy, and prophecy, do not make this signature noise.
 * In the Elenium series, use of magic can be detected in much the same way, but the range of detection seems to be much less. It's also possible to tell which spell is being used by the feel of it. Notably, the Bhelliom leaves a mark with its passing that any god or similarly powerful being can't help but feel, and using its power draws the attention of all such beings. This necessitates the protagonists to keep it in a gold box most of the time, which nullifies the effect.
 * Channelers in The Wheel of Time series can always tell if someone of the same gender is channeling nearby, and how strongly, but need to see the flows of Power in order to determine the nature of the weave used. Both the ability to channel and the weaves themselves can be concealed, by methods long-lost but rediscovered partway through the story.
 * Wizards in The Dresden Files can use their True Sight to see exactly what is going on. The Sight shows everything that's happening, in excruciating and often maddening detail, and one of the things that can be Seen is the residue of magic that has been used recently.
 * Played with in the Mistborn series: a Misting who can burn bronze (known as a "Seeker") can detect Allomancy, but a Misting burning copper (a "Smoker") can hide it.
 * In Tamora Pierce's Tortall Universe, characters with the Sight can observe use of the Gift. Alanna also has a stone which, when held, allows her to see magic in use.
 * In For Love of Evil by Piers Anthony, Parry is tracked through France by a sorcerer who can sense when he does magic.
 * Magic in the Discworld falls under both types. Strong magic leaves strong residue, to the point that especially strong magic can leave magical fields behind that warp reality and last for centuries. All wizards, and only wizards, have the ability to see "the colour of magic" (octarine, an eighth color which is outside the normal 7-color spectrum), a color which appears whenever magic is being used.
 * Robert Heinlein's Magic Inc.. Dr Worthington is a witch smeller, who detects and analyzes the magic forces that trashed Archie's store.
 * Randall Garrett's Lord Darcy series. A Witch-Smeller can detect the taint of black magic on its caster and its victims.
 * In Katherine Kurtz's Deryni, mages work this way. They can generally tell who is Deryni and who isn't, because Deryni have mental/psionic barriers called "shields" that are detectable over short distances. Some highly skilled Deryni can disguise their shields, making them seem transparent. Ordinary humans lack these shields, so their surface thoughts are easily apparent to Deryni. Transfer Portals have a residual signature that Deryni can feel and recognize (described as a tingling sensation coming from the area of the floor/ground where the Portal is located).
 * In Harry Potter and The Half Blood Prince it is suggested that powerful wizards who actually know what they're doing are capable of the residual type; in the cave scene Dumbledore is shown to determine where the secret entrance is and the spells used on it without the use of any detection spells.
 * Linden in The Second Chronicles of Thomas Covenant has the empathic ability to sense when things in the Land are healthy or diseased. Too bad that Every. Single. Thing. in the Land is corrupted and poisoned by the Sunbane.
 * Linden in The Second Chronicles of Thomas Covenant has the empathic ability to sense when things in the Land are healthy or diseased. Too bad that Every. Single. Thing. in the Land is corrupted and poisoned by the Sunbane.

Tabletop Games

 * The spell Detect Magic in Dungeons and Dragons lets magic-users see magical auras. Sufficiently long study (and a sufficiently high roll) allows the spellcaster to determine what school of magic the magic is from, and what the magic (or magical item) does.
 * In addition some monsters had the innate ability to detect magic (as the spell), such as several types of demons and devils, efreeti, imps, gynosphinxes and so on.
 * Several psionic monsters had the ability to detect the use of psionics nearby, such as the Brain Mole, Intellect Devourer and Thought Eater.
 * In 4th edition anyone with training in the arcana skill can detect magic at will.
 * In In Nomine characters with supernatural powers (mostly angels and demons, but some special humans as well) can detect "Symphonic Disturbances" caused by use of certain supernatural powers, and/or controlled Essence expenditure nearby.
 * Shadowrun. Anyone with the ability to perceive astral space (including magicians) can "see" magic use, including spells. Awakened creatures with the Magic Sense ability can detect the presence of magic, including Awakened characters (e.g. magicians) and other Awakened creatures.

Web Comics

 * Sette from Unsounded can smell magic, though not well enough to stop her from walking right into a gossamer snare trap.