Dungeons & Dragons: The Chain Lightning spell. After hitting its primary target it arcs to the nearest target (losing 1d6 of damage), doing so again and again until it runs out of energy. The chain lightning spell was modified in 3.0/3.5; this is the first and second edition version. The new version just has secondary targets all taking half damage rather than gradually reducing damage.
In Magic: The Gathering, the card Chain Lightning is an interesting example in that the spell's first target (or the target's owner) gets to choose the next target. As long as each player is willing and able to spend red mana on the spell, the process repeats itself.
Warhammer: This is generally how lightning-themed attacks work, for example the Warplightning Cannon. An older edition's Lightning Dragons had a Breath Weapon with this effect. A later edition added a Heavens spell actually called Chain Lightning, it has a chance to jump to a second target after the first, then a third after the second and so on until it fails to jump.
World of Warcraft card game (and its short-lived miniature game) faithfully recreates the video-game-version's Chain Lightning and Chain Healing spells (the page picture is from the WoW card game, not the MMORPG). This trope is so prevalent in the card game in that many Shamans or Shaman abilities/equipments can cast Chain Lightning, dealing or healing 3 damage to the first target, 2 to the next and 1 to the last.
BIONICLE: the Makuta have Chain Lightning abilities, as do the Rahkshi of Chain Lightning that they can spawn. In BIONICLE Heroes for the DS, the fully upgraded Air weapon will do this against multiple enemies.
The Farseer hero in Warcraft 3 has chain lightning. Several neutral hostile units have a weaker version, as well.
One example is Nature's Prophet who has a global-range chain as an ultimate abilty that hits 7% harder at every jump. This spell is normally used to Globally last hit everything in vision, augmenting Prophet's tendency to obtain large amounts of income for himself.
The Shaman class has chain lightning. After hitting its initial target, it will jump to the nearest enemy, but each jump reduces the damage it does.
Shaman players also have access to a Glyph that causes their Chain Lightning attacks to jump through five targets rather than the usual three, but do 10% less initial damage.
Some of the Mobs and bosses invert this with each jump doing more damage to encourage players to spread out.
In particular, C'thun, one of the Old Gods, is infamous for his beam attack. If the entire group is standing together, the last unlucky sap to get hit by the beam can sustain up to seven million damage. Watch the carnage here.
There is also Chain Healing, which functions similar and does exactly what you think it does.
Brütal Legend features an axe modification named Chain Lightning that has this effect. The Drowning Doom's Lightning Rod unit has a double-team ability that does this too.
All Heroes of Might and Magic games have this. Succubi in the fifth game have a fire variant. It can't hurt other demons, which makes it safe to use
Chain Lightning spell in Dragon Age: Origins. Any enemy mage with this spell instantly becomes a Demonic Spider. For a few levels at least: it's the only spell whose damage doesn't increase with spellpower, so it rapidly drops off to 'ow that tickles'.
In Dragon Age II, an upgraded Chain Lightning spell is one of the easiest ways to clear the field of lower-level mooks, since even the ricochets do enough damage to kill them.
Lightning spell in Fable turns into this at higher levels. Nerfed in the sequels.
The original game has a spell that is called "Chain Lightning" but isn't actually chain lightning. Instead, it shoots piercing lightning bolts at all enemies within range for massive damage against tightly packed enemies.
An ability of the Sorceress in Diablo 2.
"Proc-ing" items that give X chance to cast X level Chain Lightning upon Attack/Striking/When Struck.
The Shock Ravager/Lightning Ravager (an electricity whip that makes chain lightning in its upgraded form).
The Tesla Spikes/Storm Spikes (tiny lightning rods that arc electricity between each other when you place two or more of them, and also get a chain lightning effect when the weapon upgrades).
The Peace Maker in Jak and Daxter's sequels. Fires a small orb of electricity that arcs upon impact and instantly kills nearly every enemy in sight.
In Champions Online, this a basic power from the Electricity set. Many/most of the Electricity powers have this chaining-to-another-target as a possible effect actually, but the Chain Lightning power itself can leap every time and to multiple targets if possible. This power is not so great on single enemies, but can bounce back and forth within a small group for some NICE damage by the time it actually finishes.
Hypercubes in Video Game/Bejeweled fire one of these to destroy every gem on the screen.
F.E.A.R.'s second expansion pack Perseus Mandate adds the LP4 Lightning Arc Weapon, a BFG that will fire an enemy-seeking stroke of lightning strong enough to kill any normal or supernatural enemy with one shot, and will damage nearby enemies around the primary target as an added bonus.
Metroid Prime had a number of "beam combos" which combined a Charged Attack from one of your elemental beams with missiles. The beam combo for the Wave Beam was the Wavebuster, a stroke of lightning which arced between multiple enemies and could be fired continuously.
The Thunder Dancer from Mega Man X 8 functioned like this.
In Mega Man ZX Advent, Ashe's secondary shot in Model A form shoots one stream of electricity that arcs between every enemy you lock onto, as opposed to Grey's which fires a homing bullet at each enemy.
King's Bounty has the Lightning spell, which initially only strikes one target.
In Mabinogi, one of the three basic attack spells is lightning bolt. While at one charge it will only hit one enemy, each additional charge added allows the player to hit one more enemy near it, though it will do less damage each time it jumps. While a player can only charge a spell up to five times, it can work in combination with up to 2 other players' lightning bolts, allowing one to hit up to fifteen monsters.
Area of effect shock damage spells on later The Elder Scrolls games do this to hit other targets.
Zapper in Purple looks like a joke, until you get at least two enemies of the same type, then it will shoot lightning that connects enemies For Massive Damage.
In Star Wars Battlefront II, the primary weapon of the Empire's jetpack-equipped Dark Trooper is a lightning cannon which, to make up for its short range, can charge its shots in order to chain up to two additional nearby targets.
The Thunder Laser in Ray Crisis does this, and you can lock onto additional enemies after firing it.
Sword of the Stars: The Emitter class of weapons is essentially this as a starship weapon. It's a fairly good backup PD weapon if you don't have (enough) proper PD weapons.
Conspicuously absent for the longest time in City of Heroes. By now, it's become a staple of the later-coming Electric powersets (Electric Melee's Chain Induction, Electric Control's Jolting Chain and Synaptic Overload and the Incarnate power Ion Judgment), but is still missing from the earliest one, Electric Blast.
The Deus Ex promo for Team Fortress 2 came with the Short Circuit secondary for the Engineer, which fires electricity and hits targets in front of Engineer, AND targets near those, even teammates. In a twist, it's extremely weak (it only does 5 damage), and its main purpose is instead to destroy enemy projectiles such as rockets, grenades, and Sticky Bombs.
Lightning spells in Magicka can hit several nearby enemies at once.
Baldur's Gate 2 lets your wizards fry opponents with this. The expansion added a mace that randomly triggers this effect when it hits an enemy.
Age of Mythology: The Son of Osiris, an upgraded version of the Egyptian's standard Pharaoh, uses this to zap enemy formations; it's good for killing columns of myth units. The Titans expansion pack gives the Atlanteans the Man O' War, a jellyfish that does the same against naval flotillas.
In League of Legends activating Volibear's ultimate causes chain lightning to appear when he hits someone.
The item Statikk Shiv builds up charges whenever its holder moves or attacks, unleashing chain lightning from the target of the first attack made that passes 100 charges.
Nami has a watery variant, which bounces from ally to an enemy and vice versa, healing allies and hurting enemies.
Vigilante8 Second Offense has this as Lord Clyde's special weapon.
Transformers: Fall of Cybertron has the E.D.K. Techvolt, a Lightning Gun that will gladly jump from one enemy to another or even seek them around corners if you're near enough to them. Sadly, while its accuracy is high, its damage is extremely low, and as a result it is a fairly niche weapon in both the singleplayer and multiplayer communities.
The Ion Disruptor in the X-Universe is an energy-hog and has very short range, but has the ability to arc between dozens of targets to deal continuous shield damage to them all, provided they're relatively close to each other. It's the best way for dealing with the copious amounts of missile spam from Missile Frigates and Bombers, as it can arc between the multi-warhead missiles. But beware its tendency to hit friendly ships, as it cannot distinguish between friendly or enemy targets.