Area of Effect

Some effects, rather than having a single target, affect everything within a given area. This area is the "area of effect", and attacks/buffs that work this way are called area of effect attacks/buffs. Popular in Tabletop Games and Strategy Games, area of effect attacks are very useful for taking out large numbers of weak enemies simultaneously. However, they'll usually avert Friendly Fireproof, adding another layer of strategy to their use. They aren't necessarily offensive in nature, either -- healing or protection abilities often work in an area of effect as well.

Super-Trope to Splash Damage, but while splash damage falls off the farther away you get from the center of the attack, area of effect attacks affect everything in its area equally. Supertrope to Herd-Hitting Attack. See also Splash Damage Abuse, when an Area Of Effect is abused to get enhanced performance out of the ability.

Anime and Manga

 * Area-of-Effect is a distinct subcategory of Attack magic in Magical Girl Lyrical Nanoha universe. It mainly consists of elemental spells that freeze/burn/etc. everything within a certain radius and massive shooting spells that produce so many projectiles, they are impossible to dodge.

Tabletop Games

 * Dungeons and Dragons is the Trope Maker, having included areas of effect (typically in the form of dragons' breath and certain magic spells) since its very first edition.
 * Champions has Area Of Effect as a Power Advantage. It's used to turn regular single target attacks into this.
 * In the Star Fleet Battles Tabletop Game, the ISC's Plasmatic Pulsar Device divides its damage over several shield sections, affecting each equally.
 * These are ubiquitous in wargames, where area of effect determines what pieces are hit by artillery shells, spells, and similar attacks. Sometimes, the distance from a certain point on the table is measured instead to see if something is affected. Warhammer and Warhammer 40 K have several round plastic templates and two "flame blast" templates (dragon breath, flamethrowers, "napalm," etc). Flames Of War uses a similar plastic piece for representing bombardment.
 * Paranoia sees fit to warn about these in the "Tips for Traitors" section: "Never let the guy with the area-of-effect weapon take far left or right flank. The temptation to turn and wipe out the rest of the team in one go is just too much."

Video Games

 * Also many of the spells in the Grandia games.
 * Hoshigami - You could even increase the area of effect of your spells.
 * Mages in Dragon Age: Origins have access to massive AOE spells, which are pretty much a necessity late in the game, when crowd control becomes essential.
 * In Nippon Ichi tile-based Turn Based Strategy games, the more you level up your spells, the larger and more complex the area of effects you can access are.
 * Flamethrowers in Valkyria Chronicles and Valkyria Chronicles II hit everything in a large conical shape in front of the unit, ignoring cover.
 * Grenades in Resonance of Fate do the same amount of damage to anything within the blast radius rather than using Splash Damage.
 * Many MMORPGs.
 * Diablo and Diablo II feature lots of spells and effects with a circular hit radius, like Nova and its counterparts of other elements (including Diablo's Fire Nova), the Sorceress's Static Field (drops every nearby enemy's HP by a direct percentage), the Necromancer's Corpse Explosion and curses, the Barbarian's Warcries (both the buffing and de-buffing ones), and the Paladin's auras.
 * The X-Universe games has the Phased Shockwave Generator, an area of effect weapon that damages ships based on how many "squares" of splash damage touch the ship. What this essentially means is that capital ships will take absurd amounts of damage because they're so huge. Terran Conflict introduced the Plasma Burst Generator, which is basically a space flamethrower that shoots fusion exhaust at the enemies, dealing AOE damage. It works pretty much like the Shockwave Generator, but it is more focused (Shockwave Generators spread out at about 70 degrees, whereas Plasma Generators spread only 5-10 degrees), and mounted on smaller ships.