Fight Magnet

"A lot of people want to kill me... I take great pride in that."

—Lassiter - Psych

Everywhere a hero goes, he finds a fight. There's always a horde of Mooks who can't wait to mug the monster, and nobody will pass up the chance for a piece of the hero. Complete strangers will pick a fight with the hero for the most trivial of reasons, and gang up en masse at the slightest excuse.

This is especially common in action movies and shows, especially martial arts centered ones. It's often used as an excuse to show a fight scene when the plot doesn't call for one.

Examples of Fight Magnet include:

Anime

This happens to Sasuke a lot in Naruto. After he assembles the Hebi, he is attacked out of nowhere by Tobi and Deidara because Deidara has a grudge against Sasuke's older brother.
- Inverted by Minato / the Fourth Hokage. He was so dangerous during the Third Shinobi World War that enemy troops were ordered to withdraw immediately if there was even a possibility that Minato might be near the battlefield.
Hokuto no Ken. Well, any shonen series, really.
It's a plot point in Berserk. The protagonist is cursed with a mark on his neck that draws demons to him like a lightning rod, and while they're no big deal to him, the few well-meaning noncombatants who follow him for too long tend to meet less-than-heartwarming fates at the hands of said demons.
Trigun heavily lampshades the way danger always seems to find Vash.
In Dragonball Z, Goku asks not to be resurrected yet again, precisely because villains seem to pop up for the express purpose of endangering all his beloved friends and planets just because he's around to fight.
Kenichi: The Mightiest Disciple: it starts after Kenichi wins his first serious martial arts match. As he was still a novice, his surprising victory attracts the attention of a local gang, and thus he becomes a Fight Magnet.
Funny how the bad guys always seem to launch their long-awaited plans just when Van strolls into town in the first half-dozen episodes of Gun X Sword. (This ceases to be true once the series shifts from its Monster of the Week introductory phase.)

Comics

In Sin City, it's apparant that most of the fights Marv gets into happen due to his opponents' aggression and not through any fault of his own. It doesn't bother him too much, considering his mental state.

Film

The Karate Kid series has several people picking fights for trivial reasons. Really, even the main villains typically had dubious motivations. It's the reason why Martial Pacifist Mr. Miyagi gets so many fight scenes.
I see you like to chew. Maybe you should chew... ON MY FIST!
Old westerns loved the classic example when the stranger from outta town walks in a bar and either bumps into someone / someone's chair or the local thugs provokes him at the bar stand until he gets an excuse to attack.
In Fight Club the members all had this as a "homework" assignment. Cue hilarious Montage.
The Line: The operation is about to go down, south of the border. Well, since we can no longer just drive guns into Mexico, we'll have to get some while were down there. Fortunately for Ray Liotta's character we got a guy who's got everything we need. All we have to do is go into this bar full of pool playing mooks and ask the bartender if we can talk to him. Of course, our guy does business in the back, but the mooks need to beat up/rob his customers. Luckily for us in addition to wads of cash, we brought a 12-pack of whippass.
- Do you think our guy (or the bartender) might have stepped up to break up the fight and therefore protect some paying customers? No. He just waits until we bust up the place (and a few heads) then calmly takes us out back and sells us the weapons.
Jackie Chan movies seem to like this trope.
Many Hong Kong Kung Fu movies are largely built on this trope
The Warriors.

Literature

Stationery Voyagers. The Voyagers themselves attract more than their fair share of attention from a whole universe that's practically run by nothing but terrorists.
Jame, the heroine of P.C. Hodgell's Chronicles of the Kencyrath, appears to be this. Several other characters think it's because the machismo of her (predominantly male) assailants won't let them admit to being intimidated by a girl.
Demigods attract monsters, hence camps to train them to survive by kicking ass.

Television

Kung Fu, Twice An Episode.
"Don't make me angry. You wouldn't like me when I'm angry."
Hercules: The Legendary Journeys: The title character.
Xena as well, appropriately lampshaded in one episode where she is attacked while breastfeeding.
The Simpsons. Upon walking into a redneck bar:

"You wanna fight?"
"Them's fightin' words."

In Family Guy, when Death Takes a Holiday, Peter takes advantage of his new immortality to antagonize a bunch of drunks in a bar.
Mal in Firefly seems to be in a bar fight or a shootout every other episode.
- Admittedly, it's not just some cosmic coincidence. In one he was caught stealing a guy's wallet; in another, he went into a patriotic Alliance bar on Unification Day wearing a brown coat - i.e. the uniform of people who fought against Unification.
  - He apparently makes a tradition of doing this every Unification Day.
Ryan of The OC seemed to get beat up at least once an episode for much of the first season. This was often lampshaded by Seth.
Avatar: The Last Airbender

Iroh: It's nice to see old friends.
Zuko: Too bad you don't have any old friends that don't want to attack you.
Iroh: Hmm... Old friends that don't want to attack me...

Highlander. Probably justified since anywhere an immortal goes, other immortals feel them coming.

Tabletop Games

In Tabletop Games this is basically Random Encounters. Tabletop game worlds are generally teeming with ludicrously dangerous monsters.

Video Games

Everyone in every fighting game ever. Sometimes there's a convenient tournament to justify the endless fights or the characters are competing over something, but often there's barely any justification at all.
The Touhou series seems to have an awful lot of characters who want a piece of Reimu or Marisa, particularly in the early stages of a game.
Hammer from Fable II lampshades this trope philosophically. According to her, if two monks were the ones to enter the Wellspring Cave when you two met they would have found nothing out of the ordinary. It was because you, as a hero, accompanied her the Hollow Men showed up. A warrior will always find battle. It serves as a mark of her character development that having gone from begrudgingly accepting pacifism to now being a reluctant warrior, she has come full circle and transcended violence to the point where she can apply deeper thinking to it.
Only two of the random encounters when wandering the map in Dragon Age are remotely plot-relevant, but the most prominent example is the horde of poorly-armed and poorly-trained refugees who swarm you just north of Lothering because they need the money from the bounty on your head.
Hawke in Dragon Age II cannot even go out to get a wheel of cheese without ending up fighting twenty-plus faceless mercenaries. Delivering a piece of mail? Mercenary horde! Meeting a contact late at night? Random assassin attack! Taking a talisman to an altar on a mountain? Legions of undead and giant spiders! Going for a stroll on the beach? Tal-Vashoth squads, raider groups, and packs of feral mabari hounds! And Hawke can't go a week without running into one insane mage or another.
- This is lampshaded extensively, too. Bodahn will comment that he's never had to clean up so many bloody footprints in someone's house before. In the Legacy DLC, Hawke will lament all the constant fights s/he gets into and Varric will reply that if Hawke went to the beach for a vacation, that would be the day an armada of angry demon pirates would show up.
Taken to an extreme in Shodai Nekketsu Kunio Kun, where not just high school students, but business men, middle aged women and even baseball fanatics want to give you trouble.
Also endemic in the Pokémon games, where everyone packing a Pokeball and a monster collection wants to do battle with you.
Just about every planet that Commander Shepard visits will involve someone wanting to pick a fight with him/her. In the rare cases where there isn't an imminent round of havoc immediately available, Renegade Shepard will find one.
Replace physical battles with battles of wits, and Professor Layton qualifies. The first game had it justified by the plot; the later games, not so much.