A ‘game hack’ can be equated to a ‘game cheat’ or a modification to a video game that allows the player/user to gain an unfair advantage  over the normal offline game or other players in the case of online games. The term may also include methods or exploits that do not require any technical knowledge or game code modification, but serve the goal of cheating in a game. - Video version of the Article.
How exactly the term ‘hack’ was adapted to describe cheats is unknown, but it is very clear that the process of ‘video game hacking’ has significant similarities to ‘computer hacking’ in that one is trying to exploit a system. However, in the case of hacking games, this is mostly done for fun and usually only on devices that belong to the person doing the ‘hacking’, often breaking the rules of the game or the Terms of Service, opening the ‘cheater’ or ‘game hacker’ up to be banned from said game.
Legal status of Game Hacking
Game hacking is entirely legal in every country in the world that we are aware of. Of course that is limited to manipulating data on devices that the person doing the game hacking owns. Gaming unwanted access to any game servers or other people’s host devices on the other hand would be a whole different case. It is entirely legal to make any kinds of changes you wish to any hardware or software you own, as long as you then do not go on to make money using said modified software to unfairly compete with its creators. Notable exception here is South Korea. – However, they only outlawed distribution not personal use of game hacks. 
Different Methods of Game Hacking
The different ways in which games can be hacked are extremely numerous, some are more popular and more common than others, some are extremely exotic and rare, but here are the main most prolific methods used by game hacking communities across the world:
Game Code Modification
The main method used in most game hacking methods is modification of game code in order to implement cheating features into an online or offline game. This applies to modded game clients, injection, memory editing, trainers and savegame editing.
Mods / Modified or Modded Game Clients are mods that are installed either with the consent of the game developer or against the will of the developer in the case of most online multiplayer games. What distinguishes mods from hacks or other cheats is that cheating features become part of the game by default and do not need to be injected, performed, activated or otherwise inserted into the game in any way, since they are part of the game. Example are: Modded APKs, iOS Mods or Modded Game Clients.
Injection is a process by which code is injected into the game memory, changing functions and behaviors . This method is mainly used on PC in the form of DLL injection which is used in a lot of different hacks, aimbots, VAC tools and similar cheating tools.
Memory editors are tools, apps and software that require root access to a gaming device and able to scam, change and manipulate a games process through the game memory. Popular memory editing tools that are able to do this are Cheat Engine, GameGuaridian, GameGem ect. In theory, almost all game hacks are possible using this vector.
A game cheating method mainly used in offline games, whereby the savegame files that a game created on save are accessed, decompiled if necessary, changed and then loaded into the game to gain advantages, such as unlimited money, skill points, stat hacks and more. Save editing allows for modification of the current game state in any way one withes to manipulate it. Savegame files will often contain game variable such as money, health, stats, which can easily be manipulated.
Trainers / Cheat Tables
Essentially trainers are automated memory editing, compiled into an executable file or app that will automatically edit game memory, usually at the push of a hotkey, to activate cheats. Memory editing tools like GameGuardian or Cheat Engine have their own trainer formats called tables or scripts that act as trainers alongside those specific tools.
Automation / Bots / Scripts
While the use of automated gameplay is not code modification, it is still a subset of cheating or ‘hacking’ games as such and in many online games the use of automated macros, scripts and bots is the closest thing you can get to a cheat for unlimited money, allowing you to farm the game 24h a day for essentially unlimited resources. The use of bots or ‘botting’ is usually done using preprogrammed bots, macro recorders or custom bot software that may allow for recording and modifying paths and farming loops.
Packet interception and manipulation is another more exotic method of game hacking: It is a process whereby traffic between the game client and the game server is intercepted, the data or ‘packets’ are modified and then sent on. In essence this technique allows for same kinds of cheats as any client-side hack, but does not necessarily require root access to the gaming device, which is useful in the case of closed systems, such as gaming consoles that have not been rooted/hacked yet and therefore are not able to run unsigned or unauthorized code or software.
Exploits are the exploiting of unintended game mechanics or game bugs to gain an unfair advantage and is commonly referred to as a kind of ‘video game hack’ as well. The most well-known kinds of game exploits are ‘loot caves’, ‘dupes / item duplication’, ‘glitches’, bugged items, bugged drop rates, bugged XP rewards, bugged quests ect. Exploits are usually very temporary and are expected to get patched, especially in online games, as soon as the developers of a game become aware of them. – For this reason game hacking communities across the web do take care to keep powerful exploits, such as god modes, unlimited loot, item dupes and similar, private and under wraps as long as possible. How ‘exploitable’ a game is depends on the engine, the quality of the coding done, server vs client-side processing and more. A relative lack of exploits usually speaks for the quality of a game at least on a technical level.
Possible and Impossible Game Hacks
There are many misconceptions about what kinds of cheats are possible in what kinds of games: Here a distinction has to be made between games that are purely client-sided (processed on the players gaming device) and games that are partially server-sided (partially processed on an online game server), otherwise known as offline and online games.
In online games your gaming device, the game client, is communicating with the game server, which is where most the important information about the game world, your savegame and your account is stored. This setup in games that require an internet connection often heavily limits the kinds of game hacks that are possible in those online game titles.
Client-side cheats are possible, which often include: Aimbots, wallhacks, bots, scripts, speedhacks, teleporting (sometimes), minor damage hacks (sometimes), semi-god modes (sometimes), VAC / ESP cheats client-side modifications, skin hacks and exploits that may lead to more powerful cheats in rare and usually temporary fashion.
Generally speaking it is impossible to hack any vitally important data, such as your health, money, currencies, inventory, stats, purchases and similar data in online games. – There are very, very rare and usually temporary exceptions, but this applies to 99.99% of all online games on mobile, PC, consoles ect. Anyone that claims otherwise is probably trying to scam you.
Offline games are entirely processed on the game client, which means everything is possible. There are no limits as to what game hacks are possible in offline games that require no internet connection.
Everything is possible: God mode cheats, money cheats, invisibility, aimbots, wallhacks, skill points, unlocks, mods and modifications of all kinds. There are no limits.
No cheats are impossible in actual offline games, assuming you have root access to the gaming device/client.
Most Popular Kinds of Game Hacks
There are too many possible game hack features to list them all, but here are some of the more well-known, prolific and popular options that have been used in online and offline games on all kinds of platforms from PC, Xbox, PlayStation, Android, iOS, Nintendo consoles ect.
Unlimied Money / Currency
Very straight-forward, this kind of game hack gives you unlimited money, gems, gold, coins, diamonds or whatever currencies and premium currencies there might be in your game. – However, most of them are fake: Namely the ones for online games. This kind of cheat is only possible in offline client-sided games that store the money data on your own device where you are able to edit or manipulate the data.
Aimbotts / Aim assist
Software designed to automatically aim or assist aim, making scoring damage and kills in shooter games a lot easier and enhancing performance in online multiplayer shooters. Certainly one of the most widely used and hated game hacks in existence.
Wallhacks / ESP and Radar Hacks
Allowing the user to see enemies, items, vehicles and other objects through walls, the ‘visual assistance cheat’ (VAC) or ‘extrasensory perception’ (ESP) hack is best known by the name ‘wallhack’, as it does allow you to see though walls and walls being a huge feature of most shooter games, the name fits. One of the most popular cheats used in modern online multiplayer shooters.
Usually means unlimited health, but often includes features such as unlimited stamina, energy, mana, stats, one hit kills and more. This kind of cheat does what the name implies: It will turn you into an in-game god, able to take on any challenge with ease.
Who does not like to do more damage? Damage hacks do just that. This feature is usually only possible in offline games, but sometimes possible in online games. The one-hit kill cheat is the most widely known damage hack by far.
Online Game Hacks / Online Resource Generators
All online game resource generators and hacks are scams and fake . There are no and there never were any online hacks or generators for free currencies, money, gems, gold, coins or other goodies in any game. – These inexistent cheats, usually for online games, are scams that will try to phish you, log your passwords, scam you into completing ‘human verification’ offers, surveys or shady malware or adware downloads. Any and all websites that claim to generate game resources or money or give you free game money or currency must never be trusted and are always fraudulent.
Fake Game Hacks
There are many more fake game hacks out there on the internet than real ones  and search engines do not seem to be able to figure them out either, so that is unlikely to change anytime soon. Besides fake generators and online hacks, there are also a lot of outdated mods and downloads, downloads that contain malware, adware and phishing apps. – There is also a lot of false advertising and similar practices going on, which is why it is extremely important to find sources for game hacks that you can trust and sticking with them. Around 99 out of 100 game hacks that you will find online are either fake, outdated, scams or outright dangerous.
Game Server Hacks
Hacking the game servers of a game that you do not own is highly illegal  and we will not cover it any further than saying that while it can be done, generally people do not want to risk going to prison for a few gems in an online game. – Also there are no online hacks or generators that have hacked any game servers to give you free game currencies or resources. That has never happened.
Video: Game Hacks
Sources / References
-  https://en.wikipedia.org/wiki/Cheating_in_online_games
-  https://en.wikipedia.org/wiki/DLL_injection
-  https://www.vice.com/de/article/pa9vjn/das-passiert-wenn-du-einem-youtube-video-glaubst-und-fortnite-cheats-downloadest (German)
-  https://www.zdnet.com/article/hacker-who-launched-ddos-attacks-on-sony-ea-and-steam-gets-27-months-in-prison/
-  https://uk.pcmag.com/games/86425/south-korea-makes-game-hacking-illegal
-  https://cyware.com/news/cybercriminals-create-fake-hack-tools-and-game-cheats-to-target-users-login-credentials-22a6e059
-  https://en.wikipedia.org/wiki/Video_game_exploit