Familiar
A familiar is a magical spirit in the shape of an animal (or something vaguely like an animal) which serves as a loyal minion to a witch, warlock or wizard. Originating from real-world beliefs about witches, it is a concept that has been deeply invested in many roleplaying games.
Dungeons & Dragons
In Dungeons & Dragons, the presence of a familiar has been a class feature for wizards since at least the days of Advanced Dungeons & Dragons.
Back in those days, wizards had fairly mundane familiar options - cats, rats, snakes, toads, bats, ravens, etc. However, certain sourcebooks introduced the idea that various magical creatures, such as dragonets, could also become familiars under the right (DM-mandated) circumstances. Familiars were mostly a role-play tool, but there were serious penalties to be had if your familiar died - anything from the loss of levels to potentially dropping dead on the spot!
3rd edition essentially brought familiars over unchanged in mechanics - except in one detail. Now, the PC could take a feat called Improved Familiar; ordinary familiars gave a small bonus, usually a +2 to a specific skill, but Improved Familiars were more powerful, combat-capable creatures. The precise list of Improved Familiars and alternative familiars grew over myriad sourcebooks, to the point that players could have beasts like hippogriffs and worgs under their command.
4th edition changed that by completely removing the familiar at first. As they pointed out, familiars had traditionally not been very well regarded; they were most ignored by players and considered more of a detriment than an advantage, since they were so frail and inflicted so much damage on the player if they died. Familiars didn't resurface util the Arcane Power sourcebook, where taking a familiar became a Feat available to any Arcane class. Now, your familiar can switch between a passive move, in which they are sharing the player's space and immune to attack, or an active mode, in which they can move independently and use a special power depending on the familiar. For example, spiders can be used to haul small objects to different places with their webbing, whilst ravens can become living videophones for you Plus, if your familiar gets killed, it automatically comes back to life good as new the next time you complete a rest.
5th edition mostly takes its lead from 4th edition. Familiars are no longer a default option; instead, arcanists have access to a 1st level spell called Find Familiar, which summons a magical spirit in the form of one of various little beasties. It no longer can attack, but neither can it be killed permanently and its death has no negative effect on you. Its main use is to serve as a spy and as a conduit for spells that normally have a range of "Touch".
Pathfinder
Pathfinder's take on familiars is essentially the same as in D&D 3rd edition, though the way classes interact with them is a bit different: now wizards can pick between them and a Bonded Item that gives them an extra spell per day, sorcerers don't get them at all (though actually having class features now does help salve the pain), and it's the witch class that relies on them as a quasi-spellbook. Also, thanks to the archetype system, a few other classes can pick them up.
Warhammer
In both Warhammer Fantasy and Warhammer 40,000, familiars are a kind of lesser daemon that Chaos Sorcerers have traditionally been able to take as wargear. Daemonic familiars come in a vast array of shapes, but over time have had their roles simplify. For example, Warrior Familiars are unusually strong and aggressive for their kind, and generally provide some free attacks to their master.
In 2nd edition Warhammer Fantasy Roleplay (the one by Black Industries), familiars are discussed in "Realms of Sorcery", the sourcebook on wizard PCs. Familiars are the very first entry in chapter 7, "Magical Tools": according to this book, there are three ways to get a Familiar in the Warhammer world.
Firstly, you can craft a homunculous; a little artifical man or beast made from artificial material (or flesh & bone, if you wanna be gross) and then bring it to life with magic. This option requires Magic (3), Academic Knowledge (Magic), and Arcane Language (Magick) to have both the raw power and the learning to complete the ritual, as well as the magical affinity for Death, Fire, Light, Metal, Shadow, Chaos or Necromancy magic in order to breathe life.
Secondly, you can use magic to form a soul-bound with a living creature. This is easier than making a homunculous, as you only require Magic (2) and the Charm Animal skill, but it is restricted to those with the magical affinity for Beasts, Fire, the Heavens, Life, Light and Shadow magic, or those who possess the Witchcraft talent.
The third option is to summon and bind an imp-level Daemon - these methods are only undertaken by Chaos Sorcerers, for obvious reasons, and are detailed in the splatbook Tome of Corruption instead.
The big reason for bothering with this? Firstly, companionship; being a wizard is a lonely affair in the world of Warhammer. Secondly, every familiar has at least one of several magical bonuses:
- Aethyric Reserve allows a familiar to store a spell and then unleash it on its own.
- Link of Psyche gives master and familiar a telepathic bond - which, aside from being useful for using your familiar as a spy, also boosts both the wizard's Int and Willpower stats and the familiar's own whilst they're both conscious.
- Lucky Charm causes the familiar to generate 2 Fortune Points per day.
- Magic Focus allows the familiar to double an attribute of a spell, at the cost of making it more unpredictable.
- Magic Power means that the familiar's presence effectively raises the wizard's Magic Characteristic by 1.
- Master's Touch allows the familiar to serve as a "stand-in" for casting the wizard's spells.
- Master's Voice allows the wizard to project their voice through the familiar from afar, which means it can effectively act as not only a living telephone, but also let the wizard cast even if he's gagged.
- Voice of Reason makes the familiar into a natural magical dampener, giving its master added protection against Tzeentch's Curse.
Deadlands
In the Deadlands roleplaying game, having a Familiar is a 5-point Huckster-only Edge found in the splatbook Hucksters and Hexes. With this Edge, the huckster forms a spiritual and mental link with a single small animal - no bigger than a medium-sized dog. The familiar's presence boosts the huckster's ability to manipulate magical energy, giving them a +1 to Hexcasting rolls. However, if it's slain, that spiritual link causes a huge backlash; the Huckster must make an Incredible (11) Vigor check or be Stunned until they can pass it, and even after they shake off the stunning, they suffer a -2 modifier to all Trait and Aptitude rolls for the next 1d6 days.
Add in that it costs triple the Bounty Points and a month of study and a Fair (5) Academia: Occult roll to replace a dead familiar, you better be treating it right, partner!