Van from Gun X Sword is this, both pre-series and during.
Kenshiro of Fist of the North Star fits this trope to a tee, especially at the beginning of the series. He wanders the post-apocalyptic landscape from town to town looking for his kidnapped lover, has his sidekick in Bat, is theoretically not looking for trouble, and yet somehow always leaves behind body counts that range from dozens to hundreds.
The protagonist, Ginko, from Mushishi (a sort of mononoke-ologist)
Dr. Tenma from Monster (slightly subverted as any troubles are almost always connected with the "monster" Johan).
Raven Tengu Kabuto, from the anime of the same name. The above description is almost a plot synopsis.
Vash The Stampede of Trigun has this as pretty much his whole thing, except he's also a wanted outlaw and an immortal mutant freak.
Since his setting is Western-inspired and he has mad gun skills, Chronic Hero Syndrome and multiple issues with settling down, he does a lot of this, especially in the anime which put of the Cerebus Syndrome a lot longer, although most of the story is consumed by the plot happening.
He only stops the drifting thing during his 10-Minute Retirement after he inadvertently shot the moon, when he grows a Beard of Sorrow, changes his name, and doesn't kick the asses of the creeps who come to his new hometown and start killing everybody who annoys them. Which is kind of extreme restraint, given the town couldn't build enough coffins to house all their dead.
Interestingly, that situation gets resolved by Wolfwood drifting into town looking for him the same day Vash's adopted family member is kidnapped, and then both of them kick ass and walk off into the sunset. Vash's But Now I Must Go costs him a lot more than usual this time.
Rurouni Kenshin: The titular character purposefully became this after the war and settled down starting on the first episode. We see him comment that with the friends he makes, he may stop wandering. Also, "Rurouni" can be translated as wanderer. So Yeah.
In the Jinchuu arc, Sanosuke decides to leave the main cast temporarily and relieve some stress, which he does by becoming one of these. He then takes this time to save a town, beat the shit out of two hundred men, and terrorize the local yakuza. His stress being relieved, he then leaves town and returns to Tokyo. And nobody even knew his name.
Except his dad. That was his hometown, though he hadn't been there in over a decade.
Amusingly, the fallout from this adventure later causes him to need to flee Japan, so given his temperament he probably goes around being this in countries where no one can understand a word he says. Everyone understands when you punch a wall and the house shatters, though.
While he's mostly a Wise Prince, Ashitaka from Princess Mononoke has shades of the Drifter, as he becomes entwined with and takes a stake in the outcome of the conflict between the various factions he encounters during his travels.
As Eboshi says when asked if she saw him come around: "Came, and went."
Kanbe in Samurai Seven shows signs of being this, although the town actively recruits him and he puts up a lot of resistance.
The titular Kino of Kino's Journey, travelling the world on her talking motorcycle, with a strict rule to never stay in one country for longer than three days.
Naturally, it happens in Preacher. Jesse Custer indulges in this trope when he drifts into the town of Salvation.
The comic books spun off of the original The Legend of Zelda give this sort of backstory to Link, who happens to wander into Hyrule from his native Calatia just as Ganon is starting to wreak havoc.
Groo The Wanderer. Slightly subverted in that he's always looking for a fray.
Douwe Dabbert always ends up helping and protecting people wherever he goes.
In Nomad, Darca Nyl ends up giving this impression. He's actually trying to track down the man who killed his son, but along the way people keep thinking that he's a Jedi, and needing his help. And he gives it, and it's the only good thing he's felt in a long time. In the end, once he kills the man, he decides to take up this trope/become a Knight Errant.
The heroes in Sin City have the demeanor of the driufter (quiet loners with troubled pasts), even if they tend to stick to the city limits of Basin. Wallace might be an aversion since his story seems to indicate that he is relatively new in town. He doesn't seem to grasp how corrupt the city is and despite his deadliness, he is a relative unknown.
John J. Macreedy in the classic film Bad Day at Black Rock, although he arrives in the titular town with a specific purpose in mind (which is not to clean the place up.)
The first paragraph describes fairly accurately John Rambo in First Blood, right down to being harassed by the law. Only his subsequent actions are not to help the town at all...
Max from the Mad Max films. Shane in black leather.
High Plains Drifter plays with the conventions of this trope a bit, mainly in that The Stranger (as he is credited) is hinted at being the ghost of a man murdered by the townsfolk (indirectly) years prior and thus brings on a little vengeance by turning the town's folk against each other, manipulating and scaring them into giving him absolute power and pretty much ruining the town's economy (by blowing up the hotel, tearing down the barn and not paying for any of the many goods and services he takes advantage of, such as buying everyone in town a drink from the bar at the bartender's expense. In fact, he's barely in the town for ten minutes before he kills three men, drags a woman to the barn and rapes her.
Indiana Jones acts somewhat this way in Temple of Doom.
Sanjuro, in Kurosawa's Yojimbo (the prototype for For a Fistful of Dollars) and Sanjuro.
Also Zatoichi, hero of a long-running series of Japanese films. In each film, he wanders into a new Adventure Town, where he at first pretends to be a simple itinerant masseur and gambler. But when some local yakuza boss or corrupt official threatens him or the group of innocent commoners he's befriended, he reveals himself to be a master swordsman and all-out badass. Oh, and he's blind, too.
The animated film Kung Fu Panda starts off with a dream sequence where Po fits this trope PERFECTLY. Of course, this is just his dream self, but it does seem to show how Genre Savvy he is. Two tropes for the price of one?
The Jon Shannow/Jerusalem Man series by David Gemmell personifies this trope, often three or four times a novel.
Malik ibn Ibrahim, the protagonist of the ebook anthology Wandering Djinn, never actually looks for trouble during his wanderings, but will do what he knows is right if necessary.
Frank Chambers of The Postman Always Rings Twice starts out as a drifter who gets work at a small California diner/gas station. He is far from heroic, however.
Eiji Hino is only said to be a drifter before Kamen Rider OOO starts, since he stays in the same general area for most of the series, but he goes back to that lifestyle in the end - only now he has a group of friends to stay in touch with.
The Winchesters (and other hunters) in Supernatural.
The Winchesters more than most, because they have less of a home base than the majority of hunters, and are unusually kind and personable...even if they are violent maniacs with no respect for the law who lie like they breathe.
This is a typical trait for Prometheans. If they settle in any one place for too long, Disquiet starts to take hold in the townspeople and Wastelands bloom up under their feet. Hence, they're constantly on the move, only staying long enough in any one town to enjoy contact or refresh supplies without polluting the land or warping people's minds.
One of the playable archetypes in Feng Shui is The Drifter. He even has the ability to show up exactly where and when he is needed. In game terms, he announces he wants to show up, and everyone picks a reason how he got there. He picks the one he likes the best.
Bartz from Final Fantasy V starts off as one of these, with his pet Chocobo, Boco. This was actually his deceased father's last request.
Shadow from Final Fantasy VI actually has a chance to just take off and leave your party after every battle.
Nearly every Fallout game has you playing some variant on this character type.
Similarly to Fallout, The Elder Scrolls IV: Oblivion allows you to wander the countryside, picking up whatever quests you want, joining any/all of the five main factions, or whatever else you can think of that has nothing to do with the main story.
Shiren the Wanderer fits this well. All of the Wanderers (not just Shiren) are always on the move. In fact, its a gameplay feature: if the player stays too long in a single floor they hear a gust of wind, telling them to move on or suffer a Non-Standard Game Over. Also, backtracking is rarely a good idea, because no items spawn in the level and you end up fighting more monsters. It's all there to ensure that you always keep on the move...
Webcomics
Claudita seems to be just drifting around trying to figure out Eman Cruz and drift wherever he goes.
The episode "Zuko Alone" of Avatar: The Last Airbender pegs Zuko squarely into this role, or at least when he's not busy interrupting the above mentioned plot with flashbacks about his tragic past. In a subversion, the inevitable I Am Not Left-Handed moment reveals to the rescued townsfolk that said drifter is Fire Nation and they promptly shun him, leaving him to thanklessly drift on.
