Action Initiative

Sometimes, actions have a system of which goes first. This is important when certain actions should occur at the same time, as one could have priority over the other.

In some turn-based RPGs, every character participates once in every "turn" of combat; characters with high "Speed" generally get priority on who goes first.

One of the attributes that determines Character Tiers in fighting games is a character's (or his/her attacks') priority over other characters/attacks.

Card Games

 * In Magic: The Gathering:
 * Combat damage between creatures normally occurs simultaneously. Some creatures have an ability called First Strike, which means that their damage happens before the other one can retaliate- if the first strike damage is fatal, the victim doesn't get to deal any damage.
 * Those who delve deeply enough into the inner workings of the game's rules will learn about the system of layers that determine how continuous effects interact with one another (just in case you have an Urborg, Tomb of Yawgmoth with Blood Moon, Humility, and Opalescence on the field when somebody casts Rude Awakening and Mirrorweave... hey, you never know).

Tabletop Games

 * 1st Edition Dungeons and Dragons had a Weapon Speed Factor, which determined which combatant would hit first when they tied for initiative.
 * And later editions still have it to determine turn order. As you might imagine, acting quickly is important.
 * Champions. When more than one character can act during a segment, they act in order of Dexterity (highest to lowest).
 * Shadowrun. Characters act in order of their Initiative, highest to lowest. If two or more characters have the same initiative, tiebreakers include having the highest adjusted Reaction and the highest natural Reaction, in that order.
 * Dark Conspiracy. When two or more characters have the same Initiative, they act in descending order of adjusted Agility.
 * 1st Edition Cyberpunk 2020. All characters acting within the same phase did so in descending order of their Reflex stats.
 * GURPS 3rd Edition. The combatants acted in descending order of their Move scores. In case of ties they acted in descending order of their Basic Speed scores.
 * Warhammer 40000 has an initiative stat for all close-combat capable units, as well as various Psychic Powers and electric shocks that influence it, weapons that are unwieldy enough to reduce their wielder's initiative, etc.
 * Warhammer Fantasy as well. In the eight edition, a special rule allows one to always strike first regardless of initiative, and if initiative would have made them strike first anyways, it allows re-rolls instead.
 * In Chaosium's "Basic Roleplaying System", combatants acted in descending order of their Dexterity.
 * Legend of the Five Rings has an interesting take of this trope. Actions are resolved round-by-round, and are announced from the slowest character to the fastest, so that the faster characters can response to the action of the slower characters.
 * Deadlands, in-keeping with The Western flavor for which it was known, resolved initiative by drawing from a deck of 54 playing cards—leave the jokers in—with faster characters getting up to five cards per combat round. Rank and suit all played a role in determining who acted when. A simplified version of this system would later be used in the publisher's more generalized rule system, Savage Worlds.

Video Games

 * Pokémon: there is an abundance of moves related to priority, such as Quick Attack, Aqua Jet and Mach Punch, in addition to items and abilities. See this guide for the mechanics.
 * Super Smash Bros.: this is what determines a lot of tier rankings as well. One of the reasons why Captain Falcon is severely nerfed in Brawl compared to his previous incarnations is because the priority for many of his attacks was lowered so much.
 * In Skies of Arcadia, healing, defensive, and shielding super moves (as well as two ultimate team moves the player can use later on and a certain move used by the Final Boss) always happen before any other moves, regardless of character speed.
 * Turn order in Shining Force is based on the characters' speed stat.
 * One of the things that determine Character Tiers in the Capcom vs. Whatever fighting games. Dan Hibiki usually ends up being a Lethal Joke Character because his attacks have priority over everything.
 * The Golden Sun series has several Djinn that work this way - any damage-lowering Djinn such as Flash will be the turn's first action, as well as others such as Breath who are coded to "go before anyone else can act". Using two in one turn results in the characters' Agility being used as the tiebreaker. Notably, there are very few enemy moves that have this effect, while at least seven Djinn so far work this way.
 * Penny Arcade: OTRSPOD had a roll for initiative before each fight giving a random number between 1 and 20. A natural 20 started that character off with a full action bar.

Webcomics

 * Lampshaded like crazy in The Order of the Stick; a fight will start, someone will get initiative, then they'll talk about it for 4 or 5 frames (since Talking Is a Free Action), but someone will point out why they actually have initiative, and... "Sneak Attack!"