Reputation is the opinion towards the player character of a specific group of people.
Reputation in Fallout 2 is a way to measure general feeling for your character in each of the towns visited. Reputation can be modified by doing good or bad deeds, like completing quests or killing townsfolk.
Fallout: New Vegas
There are many different factions in the Wasteland, and you can develop a distinct relationship with each one. As you perform actions that benefit a group, you will gain Fame. If you perform actions that harm a group, you will gain Infamy. Your reputation with any given group is a measure of the combined total of Fame and Infamy that you have earned. The benefits and drawbacks of any given reputation depend on the group itself. You may receive discounts with merchants, provoke attacks from hired thugs, or simply be treated differently.
Originally, any faction member could be killed without loss of reputation, though only if the player character remained [HIDDEN] or in [CAUTION] for the kill without it progressing to [DANGER]. This was changed in the December 14th update. Players now lose reputation for killing a faction member regardless of a successful sneak kill unless that weapon is silenced and the player remains completely hidden.
However, due to an as-yet unfixed bug, the faction reputation can reset at an unpredictable time. With every faction except Goodsprings, the Boomers, Novac, and The Strip (needs verifying) your reputation will reset to neutral. However, any faction that was hostile towards you will remain so, despite the change. Support items like the NCR Emergency Radio will also become useless, and faction privileges like the McCarran monorail will be lost. There is no real way to fix this on consoles, apart from either restarting or reloading an earlier save, confirmed to happen on both casual and hardcore play modes. Some think that the reset of reputation is caused by committing an infamous act towards a faction while wearing that faction's clothing. For example, if killing a Powder Ganger while wearing a uniform of theirs, it might reset all faction reputations.
The aforementioned bug has been confirmed on all platforms: A possible solution is to travel to the Mojave Outpost, put on non-faction clothing/armor, go to where Major Knight is located, save and then speak to Major Knight; select the speech option asking if there is anything you can do to help. If your reputation with the NCR is above neutral, he will reply that you have done a great deal in a short time and advise you to ask around. Once the dialogue is complete, check your Pip-Boy. Your reputation will probably have reset from neutral to the proper standing. However, once you put on an NCR faction armor/clothing, there is a chance your reputation will reset back to neutral again. This tip can be useful however if you need to gain access to the NCR Ranger safe house or to use the monorail, or for additional help during the You'll Know It When It Happens quest.
Until the release of Lonesome Road, there was no way to get idolized by the Brotherhood of Steel. Selecting the option to abort the missile launch can get the Courier idolized by the Brotherhood if liked well enough.
Reputation in the Fallout 76 content update Wastelanders is a system that linearly logs both the good and the bad of the player character's actions with the two main factions of living humans, the settlers and the raiders. Positive dialogue choices and completing quests and dailies for the faction are surefire ways to gain reputation. Killing members of that group will bring the reputation down.
There are 7 reputation ranks: Hostile, Cautious, Neutral, Cooperative, Friendly, Neighborly, and Ally.
Reputation in Wastelanders also includes special faction items, available for purchase after certain ranks are achieved.
Reputation in Fallout Tactics is the reflection of what people think of the player character, based on their actions. Characters start with the reputation of a Warrior and move up or down from there.
Reputations, or epithets, in Van Buren are titles that can be associated with the player character based on their actions in the wasteland.