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In Bleach anyone with even a hint of spirit energy is even tastier (and easily sensed) by hollows, since they'll absorb their power when they eat them. The protagonist starts off having a small amount, but no way of using it. Eventually leading to an accidental Emergency Transformation when he absorbs Rukia's powers after she's injured protecting him and his sisters.
JoJo's Bizarre Adventure establishes this as a rule in the fourth arc. Stand Users will attract other Stand Users. It is simple fate.
The protagonist of Mushishi is able to sense mushi, weird magical life forms, but they're able to sense him, and so he must always travel lest he attract too many mushi to one place.
Monster Allergy. Zick sees monsters other than tamers, and he attracts spirits.
In Lanfeust, both the hero and the Big Bad share the same ultimate power and can feel when the other uses it. So of course Lanfeust must avoid using it at all during his journey (except one time as a lure in the frozen north, that ends up with the Big Bad teleporting there, then teleporting right back, butt-naked and demanding warm clothes).
Doctor Strange's strongest spells invoke the aid of various cosmic beings. Some of them have taken issue with him over the years.
Pokemon Master: After the Forbidden Pokemon are released from their prison the characters can not use their elemental powers freely because using elemental power draws the Forbidden's attention and lures them towards you. And you do NOT want that.
Films — Live-Action
In Inception, if the dreamer changes the dream too much (which will appear to be like magical power to an unsuspecting person in the environment), "projections" (subconscious creations) of other people in the dream get more aggressive and attack if enough changes are made.
Discworld magic draws the Things from the Dungeon Dimensions, although you have to go fairly overboard to make a path large enough for them to come through. This seems to be a bigger problem for wizards than witches, and hasn't been a serious threat since Sourcery.
In The Fellowship of the Ring, Gandalf is reluctant to use his magic during the Fellowship's trip south because it could draw attention to them, not through any supernatural means, but simply because any mundane observer can connect the dots between "hey, look at that obviously magical fire which is visible from a long way off!" and "I bet that guy who is famous for doing magical things with fire is around."
In the more typical supernatural sense, wearing the One Ring attracts the Ringwraiths.
In Percy Jackson and the Olympians, monsters can smell demigods from far away, and they try to attack them. For some reason modern technology makes it worse; cell phones are banned at Camp Half-Blood because using them will attract monsters.
Myrddraal and gholam have an ability to sense channeling. In the case of gholam this is particularly dangerous, since they are immune to channeling and were created for the express purpose of killing enemy channelers.
Monster in the Blight presumably have the same kind of fear reaction to a channeler that a normal person has to shadowspawn, though this always translates into violence, and they will come for miles to kill a channeler.
In The Sword of Shannara Trilogy by Terry Brooks, Allanon gives Shea the Elfstones with which to protect himself, but only warns him much later that using the Elfstones will alert the Warlock Lord and his Skull Bearers of Shea's location. He does this precisely so that Shea will not be afraid to use the stones if he really needs them, and because the stones themselves are an effective defense against the Skull Bearers.
In Tanya Huff's Smoke and Shadows novels, Tony Foster, who already seems to be a Weirdness Magnet, finds that he attracts even more supernatural phenomena once he becomes an actual wizard. His vampire ex-boyfriend (need more be said?) warns him that now that he is "a player" he stands out from the ranks of ordinary humanity and will inevitably attract attention. Not that Tony didn't have a history of stumbling into the supernatural anyway.
In Simon R. Green's Nightside series, if John Taylor uses his ability to find (and take) literally anything, his future enemies will find him and send the Harrowing after him.
In The Belgariad and The Malloreon, magic creates a noise that those with the skill can hear. For this reason, the party often had to avoid using much magic because other spell users would hear that noise, and although their enemy's individual casters were vastly inferior to any of them, there were a lot of them. Other times, they would have to use "quiet" spells like shapeshifting or intentionally use "loud" spells as distractions. Strong ambient magic also makes similar noises, and these can allow certain levels of magic to be "drowned out", allowing them to be used safely.
In Pact, most malevolent supernatural creatures have been bound by the Seal of Suleiman bin Daoud, which prevents them from going after innocents without cause. However, nobody who is aware of the existence of the supernatural or who practices magic qualifies as "innocent," meaning that most targets for malevolent Others are practitioners.
The danger from demons seeking to possess a witch is apparently one of the major hazards for witches in The Secret Circle.
Myths & Religion
Some Christians and others believe that involving yourself in occult activities (such as playing with an Ouija board, or wearing Satanic symbols) works, hence being magic, but gives demons free access to your soul.
Warhammer 40,000: Any Psyker risks summoning a giant monster from the Warp every time s/he uses a psychic ability.
In fact, that's a common way of Total Party Kill in Dark Heresy. In the tabletop game, anytime a psyker uses their powers they have to make a "Perils of the Warp" roll, and if they fail they get attacked by a demon that will, at best, simply make their brain explode and at worst, will inflict a massive psychic explosion.
As a matter of fact, this is why being a Psyker is Blessed with Suck in the Warhammer 40000 universe; because getting eaten by said giant monster from the Warp is the least of everyone's problem, as eventually that will cause the Psyker to become a portal to what passes for Hell in the setting, summoning The Legions of Hell, and ending up having the entire Planet becoming an Eldritch Location. In short, Magic Is a Monster MagnetUp to Eleven. Small wonder there is an entire organization granted unlimited power just to find Psykers.
Warhammer magic (especially in regards to Chaos corruption) functions the same as in Warhammer 40000, though to a lesser degree. These examples suck even worse because psykers/mages are also vital to ensuring the survival of humanity, so they can't just be rounded up and exterminated.
Using (or in some cases even possessing) psionic powers can draw psionic monsters to attack you, such as cerebral parasites, intellect devourers or thought eaters.
Phaerimm in Forgotten Realms need ambient magic and are very magic-sensitive. Consequently, casting spells on infested territories is a good way to get the nearest spell-grub to either kill the caster or capture and turn into an incubator. The same goes for enchanted items, though at shorter range. Exclusions are elemental magic (it mostly blends into fluctuations of natural forces) and Shadow Weave magic (it doesn't use the same power source).
Ravenloft setting. When in the Nightmare Lands, casting a spell can draw the attention of powerful dream monsters such as members of the Nightmare Court.
Call of Cthulhu supplement Cthulhu Companion, adventure "The Mystery of Loch Feinn". While in the underground area of Castle MacLaireag, any spell casting doubles the chance of a lloigor detecting and attacking the investigators.
GURPS Bestiary. The Octofly can detect and is attracted by psionic activity.
Earthdawn. Casting spells using raw magic can draw the attention of a Horror and cause it to Horror Mark the caster.
Shadowrun supplement Bug City. After Chicago was overrun by insect spirits, a nuclear weapon detonation put the spirits into hibernation. Using any form of magic near them can cause them to wake up and attack you.
Mage: The Awakening has Abyssal intruders, things from the anti-reality outside of our dimension. It's something of a multi-step process — vulgar (or blatantly obvious magic) risks Paradox, and really, really bad Paradox risks Abyssal intruders.
Promethean: The Created has Pandorans, the botched miscarriages that happen when the Promethean creation process goes horribly wrong. They're attracted to the Azoth that powers Prometheans, which means using powers when there's a slumbering Pandoran nearby is risking throwing up an "All You Can Eat" sign.
Rifts makes magic a magnet for genetically engineered psychic police dogs.
In the Warcraft universe it can attract demons, among other things.
In the first StarCraft terran campaign, psionic powers act this way towards the zerg. It turns out that the zerg were really looking for a psionically powerful human, rather than simply being attracted to the power itself. Once such a person is captured, the zerg stop chasing psionics.
Mages are constantly at risk of being possessed by the demons of the Fade, turning them into abominations. This is the main justification for the Templars to take them from their families as soon as their talents manifest and send them to the Circleof Magi, who train them TO hone their abilities and resist succumbing to possession. The final test for Apprentices is to undergo The Harrowing, where they are sent into the Fade and pitted against a Demon. If they succeed, they have proven themselves capable of withstanding demonic influence, but if they fail, they are immediately slain by the Templars.
The Tranquil are Mages who have undergone the Rite of Tranquility, essentially a magical lobotomy, severing their connection to the Fade which removes their powers, along with their emotions. Mages who are considered too weak-willed or dangerous are forced to become Tranquil, although it's not unheard for those who fear their abilities and do not wish to undergo the Harrowing, to choose to willingly submit to the Rite.
In Dragon Age II, this is a particular problem for Feynriel, who has a rare Dream Weaver power that hasn't been seen in centuries.
In the Diablo universe, using magic attracts demons, but then so does going for a walk or having a quiet dinner at home...
In Clive Barker's Undying, it's mentioned in the backstory that excessive usage of the Gel'ziabar stone will cause the user to be hunted by the Hound of Gel'ziabar. This doesn't actually happen in gameplay, although the Hound does pop up during a couple pre-scripted events.
According to Word of God, creatures like Skarrows, Flickering Stalkers and Monto Shonoi are interdimensional squatters, magic scavengers, that were attracted to Oneiros and the manor, and later enslaved.
In Final Fantasy XI, the arcana family of monsters (which are implied to be magical constructs) are aggressive to magic casting.
In Final Fantasy XII, Wild Elementals (which run the whole gamut from Fire Elemental to Holy Elemental to LeamondeElemental) are usually placid spheres of coalesced Mist, and will leave you alone if you do the same. But they will make a beeline for the party if anyone in the area casts a spell, whether it was you or the enemy. They're extremely vicious, will NOT let up until it or its targets are dead, and typically cast high-level magic. Unless the party is very, very strong, it's generally a good idea NOT to cast any magic whatsoever while these bright bursting balloons shimmer in the vicinity.
In multiple Final Fantasy games, but especially the Ivalice-set ones, Mist is both a conduit and a byproduct of magic, and it can summon, mutate or just plain drive wild nearby monsters.
In Kingdom Hearts, Leon mentions that The Heartless are so afraid of the Keyblade that they'll attack Sora as long as he continues to wield it. (not that he has much of a choice.) It raises the question: Why would they want to go anywhere near something they're so afraid of? The fact that keybearers have extraordinarily delicious hearts is a plot point. Also, keybearers have the power to make a World's Heart inaccessible to them.
In Persona 4, Shadows only attack Persona-users in the TV World, except for the rare days where the fog of the TV World lifts (creating natural deadlines to rescue anyone trapped there). They're normally blinded by the fog, but Persona-users stand out like beacons.
Note that this trope most definitely does not hold true in any other Shin Megami Tensei game. Demons, Shadows, and other monsters will gladly hunt down and consume Muggles any opportunity they get.
In Our Little Adventure, when Julie used the Magicant Pendant for the first time, it sent out a huge beacon of light. Not only did the Emperor see this beacon of light and knew what it was, but some imperial mooks who saw her use it engaged Julie and her group the next day... so it doubles as Encounter Bait.
In The Monster Girl Encyclopedia, "spirit energy" is the fundamental source of magic. It's also the basic energy that all of the setting's Cute Monster Girls absorb and so are able to track. Which means spellcasters are prime targets for any monster-girl that detects their presence. Though, fortunately, monster-girls in this setting no longer eat humans, preferring instead to love and rape them.
Star Trek: The Animated Series episode "The Magicks of Megas-Tu''. The alien Megans use Reality Warper level magic. The Enterprise crew starts studying how to use magic, which eventually draws the Megans' attention and gets the crew in trouble.