The following factions are the four major players in Fallout: New Vegas. During the game, there will be an option to side with one of them or to go independent, at the expense of relations with the other major factions.
Factions that, while not large in size, still play a major role in the story. Over the course of the main campaign, the player character will have the option to recruit some of them for the Second Battle of Hoover Dam, destroy them or ignore them.
The following are members of the Three Families, which can be destroyed or spared if one chooses to do it alone instead of siding with one of the three major factions. All three of these factions run casinos on the Strip.
This table is a representation of a faction's hostility towards the Courier, and how likely they will be forgiven or not. However, the Courier must also note that the higher their Reputation with the faction, the more likely they will be forgiven (such as with yielding).
New California Republic
Followers of the Apocalypse
Kings gang members
Robert House/Free Economic Zone of New Vegas
White Glove Society
Happy Trails Trading Company
Brotherhood of Steel
Wearing any faction armor will turn reputation with that faction to neutral. For example, if "Liked" by the NCR but wearing NCR face wrap armor will return reputation with the NCR to "Neutral". It will go back to "Liked" once the armor is removed.
Faction armor may also temporarily (while the disguise is on) erase some faction relationships completely from the PipBoy. For example, wearing BoS power armor will set one's relationship with the BoS to Neutral, relationships with Freeside and the Strip will remain the same, but one cannot see any reference to a relationship with NCR and the Legion. This is not a bug, but just a way to illustrate which factions are unaffected by the faction armor. (Other factions that have been removed may either be hostile or friendly.)
Wearing faction armor is also a good way to accept quests from factions that would normally result in being attacked. For example, if having killed several Great Khans, the whole village will attack on sight if approaching Red Rock Canyon. However, while wearing Great Khan faction armor, one can accept and complete quests, which would eventually get some mixed reputation, and enough to allow safely taking off the faction armor without hostilities from that faction. It is recommended to always wear the faction armor (as much as possible) when advancing the quests to prevent quest failure or certain quest people from turning hostile. (At the same time, if one is entering an area from the opposite faction, be sure to take it off to prevent hostilities.)
The Courier can kill members of a certain faction without consequences if they sneak attack while hidden successfully.
Behind the scenes
Joshua Sawyer stated that "each of the major factions intentionally exhibits both characteristic strengths and weaknesses of their type of organization. The NCR is most like the current American government, but none of the factions are intended to be an indictment of the United States' politics/government."
PCXbox 360 Sometimes equipping any faction clothing/armor, no matter how briefly, permanently sets you as a member of that faction in the eyes of all enemies of that faction. This happens even if you put on neutral duds before exiting Pip-Boy and no non-player character ever sees you wearing enemy faction attire. For example, while looting bodies out in the wasteland you accidentally put on Powder Ganger armor, but immediately take it off. When you return to Primm all residents will be hostile anyway. If you ever put on Legion gear, the NCR will be hostile forever after, etc. This can be remedied by putting on the clothing of the faction you are associated with and taking it off. [verified]
Xbox 360 Trading faction armor you are wearing to a companion will result in an interface bug, as you are still in the trading screen when the "no longer wearing faction armor" comment pops up. (Furthermore, if the faction armor cannot be worn by the companion, as is the case for most of them (Veronica can wear brotherhood armor, and Boone can wear NCR armor), they will drop the armor anyway.) This dialogue can be impossible to select OK on. Pressing start and hitting "Continue" appears to fix this. (Unconfirmed on other platforms.) [verified]
Playstation 3Xbox 360 If you are accepted, idolized, etc., by a faction and you wear their armor, it is possible that your reputation with that faction will drop to neutral, even if you take the armor off. It is possible for it to work in the opposite way, if you're vilified, hated, etc., the same thing can happen. The only way to boost your reputation with that faction is to do quests for them. When you drop the armor your reputations will go back to normal. [verified]
Xbox 360 Upon killing a certain amount of faction characters in a legion owned location regardless of reputation, using the stealth kill method or using enemy faction armor to mask the attacks characters who can see through disguises will be hostile towards the character regardless of stealth or reputation. For example, if the player triggers this bug and has not alerted the location through unsuccessful stealth kills (the kills either were not hidden or the weapon was not silent) or does not have negative faction reputation; any character that can see through disguises (such as Dead Sea) will be hostile and alert any other legion faction character nearby to become hostile much like if the player has vitrified reputation with the legion and is disguised as legion and their disguise is compromised by a character who can see through disguises. This will also remain true for characters that are in a different area inside the location such as house or barracks those characters will function like above (such as doing this in Nelson and walking into the barracks containing the legion soldiers and Dead Sea because he can see through disguises). This will break when the player has killed all legion faction soldiers in the area (if the player kills all legion soldiers outside of Nelson including the explorers that patrol the area outside of the town the player can enter the legion barracks and find Dead Sea and his fellow legion recruits not hostile). This may or may not be a bug due to if soldiers notice a large portion of their force being kill by an unknown enemy they should search for the unknown killer but only soldiers perceptive enough to see through disguises will be able to identify him/her could be a design feature however this only seems to affect the legion and not the NCR. Locations tested at: Nelson, Cottonwood Cove, Camp Forlorn Hope and Mojave Outpost. [verified]