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.
The following factions are the 3 major players in New Vegas. During the course of the game, you will eventually have the option to side with one of them, or go it alone, to the expense of your relations with the other major factions.
Wearing any faction armor will move your reputation with that faction to neutral. For example, if you are "Liked" by the NCR but you are wearing NCR face wrap armor your reputation with the NCR will be neutral. It will return to "Liked" if you take that armor off.
Faction armor may also temporarily (while the disguise is on) erase some faction relationships completely from your PipBoy. For example, wearing BoS power armor will set your relationship with the BoS to Neutral, your relationships with Freeside and the Strip will remain the same, but you will not 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 to you.)
Wearing faction armor is also a good way to accept quests from factions that would normally attack you. For example, if you've killed several Great Khans, the whole village will attack you if you approach Red Rock Canyon. However, while wearing Great Khan faction armor, you can accept and complete quests, which would eventually get you some mixed reputation, and enough to allow you to safely take 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 becoming hostile to you. (At the same time, if you're entering an area from the opposite faction, be sure to take it off to prevent hostilities.)
The player can kill members of a certain faction with no consequences if they sneak attack while hidden successfully.
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 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 clothing of the faction you are associated with and taking it off.
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 power armor), they will drop the armor, anyway.) This dialog can be impossible to select OK on. Pressing start and hitting Continue appears to fix this. (Unconfirmed on other platforms.)
Xbox 360PlayStation 3 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, you'll still be neutral.It is possible for it to work 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.