You Have to Burn the Web

If anyone happens to use a source of ignition in a Cobweb Jungle, you'll have an inferno in seconds.

A bit of Artistic License -- spider silk does shrivel quite rapidly when exposed to intense heat (so yes, a flamethrower can clear out cobwebs), but it doesn't actually burn, much less cause the pyrotechnics that people have come to expect in fiction. On the other hand, the dust that collects on old cobwebs usually is flammable, so sometimes those dusty old cobwebs really are as burnable as fiction makes them appear. But in fiction even clean, freshly spun spider silk can (and usually will) go up in flames.

Named for a videogame. Not to be confused with the rise of the World Wide Web breaking the premise of a story.

Anime and Manga

 * Subverted in One Piece, thriller bark arc. When the Zombie spiders attack, the webs are immune to everything but fire... but they MELT. And not immediately... they just get softer and squishier.
 * In episode three of xxxHolic Kei there are a lot of spider's webs being set on fire and they even fall to the ground and continue to burn for a while. The villain comments twice on how fire and spider's silk don't mix.

Comic Books

 * Inverted in Spider Man, where said hero occasionally uses his webs to put out fires. Of course, depending on the version, it may or may not be real spider silk he's using.

Film

 * This entire trope probably originates from the fact that in old movies (especially B movies), cobwebs were typically made from cotton, and would burn quite handily if set to an open flame. Hollywood writers/directors apparently didn't realize that real webs do not work that way.
 * Gremlins 2 when Gizmo shoots the spider gremlin with flaming arrows.
 * Averted in Eight Legged Freaks, a horror film about giant spiders; there is a fire but its caused by the presence of explosive gas in the mines where the spiders have taken residence.
 * In Son of Godzilla, giant spider Kumonga (AKA Spiega)'s web is stated to be impossible to cut (not even Godzilla can slash it) but a cigarette lighter will take it out no problem (fortunately for Godzilla, he's got that atomic breath). Kumonga himself later catches on fire from repeated blasts of Godzilla's ray.

Literature

 * There's a "get through the giant web by burning it" bit in Emily Rodda's Rowan of Rin, although it doesn't ignite the whole place. Also, the minute they've burned enough web to escape, the giant spiders start repairing the hole, so getting through the "gate" there is a little unnerving and they end up brushing spiders off the last person through.
 * In one short story, knowledge of this trope was used as a trap in a virtual reality game. The player gets caught in a web, and is expected to use his flare to burn his way out. The trap is that the web is coated in some quick-burning material, so while the spiderweb itself is not flammable, trying to burn it will set off the napalm it's coated in.
 * Used in the prison Cold Open from The Bones of Haven, from Simon R. Green's "Hawk & Fisher" series. Complicated by the fact that this particular Cobweb Jungle is alive, and mobile enough to freak out when it starts to burn.

Tabletop Games

 * Some of these examples are likely to be derived from Dungeons and Dragons, where you could burn webs (and the Web spell) and do fire damage to anything caught in them. In the most recent edition, this doesn't work any more, and Webs (or, for that matter, walls of ice) will remain unaffected by heat, fire, and volcanoes.
 * In fact, the 3rd edition Dungeon Master's Guide has a short example dungeon where this method should be used to destroy a colony of spiders inhabiting a cobwebbed roof. (Or the players can not look up and notice the web, and instead get ambushed by spiders.)
 * That example is actually a remake of the example dungeon from the 1st Edition DMG, updated for the 3E rules and iconic characters.

Video Games

 * The Legend of Zelda Ocarina of Time was one of the first video games to do this, showing up in the first dungeon. Later games have used the mechanic as well.
 * And Fanfic too.
 * Mocked in this VG Cats strip.
 * Savage Empire (a spin-off of the Ultima series) did it about a decade earlier.
 * Spider webs are not burnable in Skyward Sword; or, at least, nothing is available to burn them with. You have to cut them up with your sword instead, which is extremely tedious, and half the time you get caught in the remnants of the web anyway...
 * In Resident Evil, you end up trapped in a room where the exit is webbed over by Giant Spiders, and when playing as Chris, can burn the web off the door with a flamethrower. If you're playing as Jill, on the other hand, you just cut the web with a knife.
 * It doesn't catch fire in either version, though. In the original it simply vanishes, and in the remake it pulls apart when the flame hits it.
 * Ty the Tasmanian Tiger loves this trope, and uses it as often as it can. Collectable on the level floor? You Have to Burn the Web. Arched doorway? Torch it. It gets annoying quite quickly, as your fire boomerangs are actually some of your weaker weapons, forcing you to cycle between it and a better one, often while under attack by funnel web spiders.
 * In A Boy and His Blob, one of the first puzzles is a giant cobweb that kills you if you go through it. You burn it with a torch, but the trope is somewhat averted in that the web doesn't really burn, so much as completely vanish.
 * And Yet It Moves, an independent platform rotation game, had this for one level. Made more difficult when the fire could burn your poor paper body.
 * One part of Kuon involves suddenly finding yourself faced with an entryway blocked off by silk. You already have a knife that's on fire, but in order to get through it you need to find the scissors item.
 * In Richard Bartle's original MUD, you encounter a cord in a forest. When you touch it, you discover that it's part of a giant spider's web and that you're stuck to it. Once you've done that, you literally Have To Burn The Web before the spider devours you alive.
 * Reaching the final boss monster of Cute Knight Kingdom requires learning the spell of Flame in order to burn the webs blocking the passage. It just disappears, though, no inferno.
 * Buffy the Vampire Slayer encounters webs large enough to completely cover doors in both of her video games. The only solution is to burn them down.
 * In the first of the Dark Parables games, there is a Giant Spider with an equally giant web blocking a doorway through which you must go. Naturally, the only recourse is to burn the web, but you can't do so until you acquire the necessary Plot Coupon (a torch).
 * Averted in Pokémon Black and White. Clay just has his Krokorok take out the Galvantua web in Chargestone Cave's mouth, there's no burning involved.

Web Original

 * In a later session of Spoony's Campaign, the party encounters a room full of spiderwebs and deals with them by throwing a flaming bedroll into the room. Unfortunately these were phase spiders, which meant they teleported Lord Kat's character Grae into the room with the burning webs while his friends were outside dealing with more monsters.

Web Comics

 * In The Adventures of Dr. McNinja, Dr. McNinja had this work against him once.
 * Lampshaded in the alt text: "I don't even know if spiderwebs are flammable. Again, this is Zelda basically steering this comic."

Western Animation

 * In the Futurama episode Benderama Bender gets trapped in a spider's web and has to use fire to escape.