Alliance Meter

The act of deciding which of various dueling factions you want to have as your enemies and allies, and the effect your actions have on that balance.

For instance, imagine you take a mission from Faction A to kill ships belonging to Faction B. This pleases Faction A and the allied Faction C, while angering B and their allies in Faction D. Depending on your current and desired relations with Factions A, B, C and D, this may work out to be either good or bad for you.

The simplest form of this is the Karma Meter, in games with light- and dark-side factions. Story-based alliance changes don't count; it has to revolve around actions you might or might not choose to take. You may be able to become friendly with most of the factions present, but you can't please everyone.

Compare Relationship Values for individuals, and Karma Meter for when there are only two sides. Factions that love you may give you a 100% Heroism Rating, while if you make everyone hate you, You Lose At Zero Trust. See also With Us or Against Us and Enemy Mine.

Examples of the Alliance Meter in popular media:

Action games

Grand Theft Auto 2 has three meters, one for each gang in the city. Zaibatsu always has one, while other two change according to city. Higher the respect, more dangerous(and better paying) missions player can take.
The Mercenaries games feature dynamic relations meters between your chosen mercenary and the various factions active in the warzones you fight in. Generally, doing things the faction likes (i.e. shooting their enemies in line-of-sight of the faction's soldiers, completing their missions, bringing them enemy vehicles, etc.) will please them, while openly killing their troops, sabotaging their operations, etc. will piss them off. In the second game, this only happens if the enemy manages to get in a radio call to their headquarters that you're causing havoc. If you kill the radio operator before he can finish the call, the enemy will be none the wiser. However, you'll always be hostile with either the North Korean Army or the Venezuelan Army. It's also possible to permanently make a faction your enemy int he second game when you receive missions to destroy their headquarters late game.
In Shadow the Hedgehog you have three options in each level. The good path, neutral path, or bad path.
In Famous
Present in Sid Meier's Pirates!: The game tracks your relationship with each of the four major colonial powers. Attacking one power's ships will earn you favor from its enemies and scorn from its allies. However, the political situation is constantly in flux, with wars breaking out, truces being signed, and alliances being made or broken seemingly at the drop of a hat, so if you're trying to butter up with one faction in particular, you have to pay attention to current events.

MMORPG

World of Warcraft features a reputation system, representing your character's current standing with various factions found in Azeroth and Outland. Each faction has eight different rankings, ranging from "hated" to "exalted", and NPCs react differently depending on your current rank. The higher your rank, the friendlier a faction becomes. Most capital cities of your own faction start as Friendly, while most other factions start as neutral or hostile. High reputation with a faction generally allows you to purchase goods only available from them.
In EVE Online, helping a faction or their affiliates gives you access to more profitable missions and discounts on various fees. Unfortunately, bowing to one direction usually means that you'll also moon the opposite faction. This standings system is also a crucial tool in diplomacy between players, corporations and alliances. In addition to being highlighted in the UI by everyone belonging to the organization in question, organizations with high standings can be allowed to access various structures like space stations.
Dungeons and Dragons Online has a "Favor" system where completing quests grants you a few points of hospitality from whatever patrons are in charge of that quest. The more points, the more you are favored by that patron, and each one has its own levels (typically 3 or 4 per patron) and leveling up your favor gets you rewards. It can't go back down, though, and they can't be played against each other.

Role Playing Games

Fallout 2 had an individual opinion meter for each town the player entered, along with a Karma Meter. Thus, a player can have negative karma for wiping out a town of innocents but still be loved by its neighboring town because they were at war with them.
- Similarly, New Vegas has one for major towns such as Freeside, and most factions. Your relationship with Mr. House is binary, however; he'll consider you a valued employee right up until the moment you oppose him.
In Freelancer, every mission you take affects your rep with everybody connected to either faction involved. Oddly, people pay a lot more attention to who you took the mission from that who it was against. So to continue the page example, Faction E, which is allied with both A and B, will be pleased and F, which hates both, will be angered. A Hostile faction will attack on sight and deny you landing permission on their bases; a Neutral faction will ignore you in space but might assist allies who hate you, and will let you land but might not sell you their best stuff; and a Friendly faction will assist you in combat against anyone they're not allied with, stay out of the fight when they are, and will sell you their best stuff and offer you the best missions.
- There are also guys who offer to hack your file with a particular faction through the Neural Net, making them and their allies think they like you, at the cost of angering their enemies and also the hacker charging you a bundle.
- One faction is worth noting because they hate everybody except the Zoners and the IMG: the Xenos, a rabidly xenophobic faction of terrorists in Liberty. Players often slaughter them in huge numbers to improve their reputation with almost everyone else.
- If you manage to sink your alliance meter low enough with opposing factions, it will lead to members of those groups to put aside their hatred to team up against you. Corsairs and Outcasts against you? Can see that happening. But it gets downright absurd when you get Nomads joining up with The Order to kill you.
In the Geneforge games, you can end up on either side of the Shaper War, or in some cases destroy both. Note that that doesn't work in Geneforge 5, where You Lose At Zero Trust.
The Elder Scrolls II: Daggerfall has a primitive system where your initial character build allowed you to adjust how friendly various segments of society from peasants to nobles would react to your player. In actuality, the effect was minimal. What had slightly more effect was the hidden in-play alliance meter that the character build modified, as the relation to a faction was one of the factors that decided when promotion in that faction could occur.
- The Elder Scrolls III: Morrowind has a similar system, with three main differences: the effect on an indidual NPC is greater, the number of factions are heavily reduced (no peasant faction, for instance), and very few of the quests impacting faction-relation could be done without joining a faction.

Simulation

The indie game Democracy pretty much runs on this trope. The entire society of the country you are in charge of is divided into overlapping groups like "parents", "smokers", "middle income", "commuters" etc. Every single one of the 20+ groups gets its own satisfaction meter, influenced by the policies you introduce. The meters take up the entire center of the screen for most of the game.
Vega Strike has a lot of factions, some allied and some feuding. Not only legitimate ones, but ISO and Pirates are some people's "friends in low places" too. This leaves Luddites as the Butt Monkey: everyone either hates or barely tolerates them. Blow up a lot of their ships, and not only pirates think you're a pretty swell guy despite several hits against them, but even aggressive aliens at war with the humanity give you some benefit of doubt.
Spore has them in the last 4 stages: Red faces mean they hate your guts. Orange faces mean they don't trust you. Yellow faces are neutral. Blue faces mean they like you. And green faces mean they worship you.
Master of Orion also has meters for your relations with every other race.
Tropico has political ideologies. Every citizen has certain political opinions which player must try to please to win elections. Assuming you hold elections, of course. (Though even if you don't, it's still a good idea to keep the various groups as happy as possible.)
- With the expansion pack you are allowed to Take a Third Option and outright ban one political group, meaning you are free to do things that would normally upset people of that ideology. (Then again, banning them upsets them so much that it is a "The Revolution Will Not Be Civilized" moment for many.)
In Wing Commander Privateer, your standing with the factions in the Gemini sector can be altered by which faction you shoot down. While regaining trust after a killing spree is technically possible, without Roman Lynch's help in the add-on Righteous Fire it's much more difficult. Note that Retros will never be friendly other than for plot-dictated reasons in Righteous Fire.
X-Universe games have 5 basic races / factions (6 as of Terran Conflict), with each side having different relations to each other. Killing hated enemies will give you a reputation to the sector owner and a hit to the victim, killing neutrals will give you a hit to both the victim and sector owner reputation, and killing an allied will give you a massive hit to the allied victim and the sector owner. It's possible to ally yourself with all the races, including the Space Pirates, by avoiding combat missions and not slaughtering random ships in sectors. Getting your reputation up will allow you to buy high power weaponry and ships, while low reputation will prevent you from entering their core sectors, docking at stations, all the way up to outright kill-on-sight orders.

Strategy

X-COM: Apocalypse has a lot of organizations most of whom you want to be as friendly as possible, for various reasons. Which isn't easy, because alien infiltration and collateral damage to their property make them upset.

Stealth Based Shooters

Splinter Cell: Double Agent. Your actions affect how much you're trusted by the John Brown's Army (JBA) terrorist group you're trying to infiltrate and the National Security Agency (NSA), your real employer. The amount of trust for each organization is shown on a trust meter. Oddly, since it's zero-sum, a faction will lose trust in you if you help their enemies in a way they don't even know about.
In Thief 3, there were two values representing Garrett's popularity with the Hammerites and the Pagans. They were pretty useless, however, since the only ways to manipulate them were three minor sidequests and the only effect they had on the gameplay was that Garrett's allies acted as meatshields for him during the final mission.