Reputation is the opinion of the public toward a person or a group of people.
Reputation in Fallout 2 is a way to measure general feeling for your character in each of the towns you visit. 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 of the group itself. You may receive discounts with merchants, provoke attacks from hired thugs, or simply be treated differently.
Any faction member can be killed with no loss of reputation, though only if the player remains hidden or in caution for the kill without it progressing to danger. (This has been 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, your 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 a Ps3 or Xbox, 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 factions clothing. For example, if you kill a Powder Ganger while wearing the Powder Ganger uniform, it might reset all faction reputations.
The aforementioned bug has been confirmed on all platforms: A possible solution (confirmed on Xbox 360, PS3 and PC) 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 Safehouse (say to get the Ranger combat armor), 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 Fallout Tactics is the reflection of what people think of player's character, based on his/her action. Characters start with the reputation of a Warrior, and move up or down from there.