Rooftop Confrontation

Fighting on top of buildings is totally Badass. Probably because of the risk of falling off. For whatever reason, often resulting from a Chase Scene or an attempted and botched escape (sometimes courtesy of a Climbing Climax), two characters wind up squaring off on a rooftop. Sometimes involves Roof Hopping if it takes place in the middle of a city, but sometimes a single rooftop can be just as badass, since it limits a character's maneuverability.

Marvel Comics might be the trope codifier - rooftops are handy for superheroes as they allow a fight in the middle of the city without (too many) civilians getting in the way.

Traintop Battle is a mobile variant.

Video game examples should only be added if they are particularly unique or unusual, since it's common in fighting games to have a rooftop stage that has no plot relevance whatsoever.

Examples of Rooftop Confrontation include:

Anime and Manga

At the climax of Tsumihoroboshi-hen in Higurashi no Naku Koro ni, Keiichi and Rena square off on the roof of the school.
Ghost in the Shell Stand-Alone Complex. The Individual Eleven practice a ritualized Mutual Kill on top of a rooftop; it ends with a sword-fight when one of them changes his mind. All of this is caught on tape and makes for a pretty horrifying news report.
In the TV version of Yamada Taro Monogatari (can't vouch for the manga here) Sugiura confronts Taro on the rooftop in an early episode.
- In the film X 1999, the final battle takes place on the roof of a tall building.
In volume 7 of Parasyte, Goto faces off against the military on the roof of a building. He massacres them.

Comic Books

In All Fall Down, Portia trades blows with the Ghoul on a skyscraper after he interrupts her suicide attempt.

Film

The Matrix has an epic fight scene on top of a building.
Predator II. Lieutenant Harrigan fights the Predator on the roof of a building as part of a running battle with it.
The climax of Hollywood Homicide ended up on a roof.
Subverted in Spider Man 2. A fight between Spiderman and Octavious begins on the roof of a building, but they end up chasing each other all over the city.
The original Die Hard movie has this, with the plot-relevant roof being special because it doesn't survive the fight.
The climax of Jackie Chan's Who Am I was a martial-arts fight atop a skyscraper, ending with No Escape but Down.
Last Action Hero. The climactic battle between Jack Slater and the Ripper occurs on a rooftop.
The final confrontation between Colin Sullivan and Billy Costigan in The Departed is on a rooftop, although the actual shooting happens in the lift when they reach the ground floor.
Denny and the drug dealer "tangle" in The Room. The incident itself is never mentioned again.
Batman (1989). Near the beginning the title character confronts and fights two robbers on the roof of a building where they're counting their ill-gotten gains.
Scotland, PA ends with a fight between McBeth and Lt McDuff on the roof of a fast food restaurant.
In Max Payne, the climax where Max confronts the guy who killed his wife occurs on a hele-pad on top of the Aesir Pharmaceuticals high-rise building.
In the film version of Ichi the Killer, the final confrontation takes place on the roof of the Yakuza apartment building.
The 1920 silent movie The Golem features a showdown between the Golem and Knight Florian on top of the Rabbi's observatory tower.

Literature

Lampshaded heavily in all of Robert Rankin's books that feature Lazlo Woodbine, Private Detective. Lazlo only works four locations: his office, a bar, a back alley, and a rooftop for the final denouement with the villain.
In Animorphs, Ax chases Visser Three onto a rooftop to confront him for a one-on-one battle.
Forms part of the climax in Moon Over Soho and lets our hero throw a chimney stack at the Big Bad.
The final controntation in Night Watch (the book and the movie) happens on a rooftop. The movie has Anton fight with Zabulon with a halogen lamp (Zabulon is wielding a sword he has just pulled out of his spine). In the book, Zabulon is about to kill Anton with a powerful spell after Anton has a revelation about Svetlana but is stopped.
- In the movie, the entire fight is choreographed by Zabulon to end up with Anton nearly killing Yegor by accident, resulting in the latter becoming a Dark Other.
In Shakugan no Shana, the final confrontation between Yuji, Shana and Friagne happens on the roof of an abandoned department store.

Live Action TV

Happens in a first season episode of Battlestar Galactica where Six beats Sharon up on top of a building.
Season 3 of Dexter featured a rooftop confrontation between Miguel and Dexter towards the climax of the season. It was only a confrontation, not really a fight... but it was a pretty awesome scene anyway.
Mighty Morphin Power Rangers: The very first morphed battle occurs atop a building in Angel Grove.
Although no actual physical fighting occurs, in Sherlock, Sherlock Holmes and Jim Moriarty have a final confrontation on the roof of St. Bart's in "The Reichenbach Fall."
In Soap Mary's first husband confronts Burt and tries to kill him on top of a building in mid-construction, so he can take over the constructing business.
CSI: NY Mac and Clay Dobson in one episode of a several ep arc in season 3. Mac had busted a dirty cop and Dobson was released because of the cop's testimony being tossed out. He killed another person, though, and Mac chased him down, cornering him on the rooftop. Dobson waited to be cuffed, then jumped off the roof in an attempt to frame Mac for police brutality, though it failed.

Music

"Oi! To The World", originally by the Vandals and later covered by No Doubt, is about a rooftop battle between a Middle Eastern punk and a skinhead on Christmas Day. The song ends with the punk saving the skin's life in the spirit of the season.

Video Game

In Vigilante, the fifth and final stage has the player fighting on top of girders high above street level.
Fahrenheit (2005 video game) (AKA Fahrenheit) has a fight above a roof between Lucas and the Oracle.

Webcomics

In Order of the Stick, Elan duels His father Tarquin on a rooftop after realizing that the man is evil. His adversary approves of the location choice.
Adventure Dennis has its final climactic battle take place on a rooftop.
Both the fan comic Roommates and its Spin-Off Girls Next Door had one. Sorta. The Roommates one planed by Dark!Jareth got highly anti-climatic when all heroic characters basically refused to fight him (and his own villainous deeds became his undoing). The Girls Next Door one by Erik got weird when the other characters brought the popcorn... and the heroines didn't need saving anyway.

Western Animation

Leo vs Raph in TMNT.
- Also many of their battles with the Shredder happen on rooftops in the original comics, 03 series and 90s movies.
The opening sequence of Batman: The Animated Series features Batman confronting bank robbers on a rooftop.