Fallout: New Vegas companions

Permanent companions
You can have up to two companions in your party (one humanoid and one non-humanoid). All permanent companions have a unique quest line that you can follow in order to "upgrade" them, usually giving them new armor or new perks. .
 * Arcade Israel Gannon, a member of the Followers of the Apocalypse in 2281 and can be found in Freeside's Old Mormon Fort.
 * Craig Boone, a former NCR 1st Recon sniper with a grudge against Caesar's Legion and a chip on his shoulder. He can be found at night in the dinosaur at Novac. Can be recruited after completing One for My Baby and using the right dialogue.
 * Lily Bowen, a friendly nightkin and former assassin in the Master's army. She can be recruited in Jacobstown after you get the quest Guess Who I Saw Today.
 * Raul Tejada, a ghoul mechanic and former gunslinger held hostage by Tabitha, the mad leader of the State of Utobitha. Can be found in Black Mountain.
 * Rose of Sharon Cassidy (also known as Cass), a former caravan merchant and the daughter of John Cassidy. She can be found in Mojave Outpost.
 * Veronica Santangelo, a disillusioned Brotherhood Scribe. She can be found at the 188 Trading Post

Non-Humanoid companions

 * ED-E, a prototype eyebot designed for combat and reconnaissance operations. It can be found in Primm, in a non functional state, lying on the counter inside the Mojave Express Which is labeled in-game as "Nash Residence".
 * Rex, is a cyberdog in Freeside under the ownership of the King. He is suffering from neural degradation as his old brain decays.

Dead Money companions
These companions are only available while playing the Dead Money add-on, they are only temporary and will not follow the player around as standard companions do:
 * Dean Domino, a ghoulified pre-War lounge singer. He is found in the Residential District of the Sierra Madre.
 * Christine Royce, a mute ex-Brotherhood Scribe found in a malfunctioning Auto-Doc at the Sierra Madre Medical District.
 * Dog/God, a nightkin found in the Villa Police Station of the Sierra Madre.

Honest Hearts companions
These companions are only available while playing the Honest Hearts add-on, they are only temporary and will not follow the player around as standard companions do:
 * Follows-Chalk, a novice scout for the Dead Horses tribe with wanderlust. He first accompanies the Courier for a while, before permanently returning to the Dead Horse camp.
 * Waking Cloud, the midwife of the Sorrows tribe worried about her husband. She accompanies the Courier upon Daniel's recommendation.
 * Joshua Graham, former Legate and reborn New Canaanite acting as war chief for the Dead Horses. He will only accompany the Courier during either the Flight from Zion or the Crush the White Legs final quests.

Old World Blues companions

 * Roxie, a cyberdog which you create using the available splicing machine and acquiring the correct holotape. Roxie will follow the Courier around the X-8 research center only; she cannot leave it. When you interact with her, it is only through dialogue rather than the command wheel. Unlike Rex, you cannot open her inventory to give/take things. Even in non-hardcore mode she can die, but you can then go make another Roxie.

Lonesome Road companions

 * ED-E, a cloned version of ED-E, armed with an arc welder.

Cut companions

 * Ulysses, The original Courier Six and significant character in Lonesome Road. Depending on the dialogue you choose, he will either temporarily join you or fight you.

Temporary followers
Temporary followers are NPCs who accompany you during a quest, or offer their support only for a limited time or within a certain area. Unlike permanent companions, temporary companions do not use the companion wheel, do not heal automatically, and with the exception of Deputy Beagle do not have an option to exchange equipment.
 * Body guard (hired in Freeside)
 * Cannibal Johnson (Enclave Remnant)
 * Deputy Beagle (during My Kind of Town)
 * Joana (during Bye Bye Love)
 * Logan (during part of Wheel of Fortune)
 * NCR Ranger (activated via NCR emergency radio)
 * NCR Trooper (activated via NCR emergency radio)
 * Neil (during part of Crazy, Crazy, Crazy)
 * Orris (hired in Freeside)
 * Private Halford (in Camp Guardian caves)
 * Rhonda (during part of Crazy, Crazy, Crazy)
 * Securitron Mk II (Or Securitron Mk I) (during No Gods, No Masters or All or Nothing)
 * Sunny Smiles (during Back in the Saddle, By a Campfire on the Trail, and Ghost Town Gunfight)
 * Ted Gunderson (during Beyond the Beef)
 * Victor (during We Must Stop Meeting Like This and We Must Stop Beating Like This)

Nerve
Each companion also has a special attribute referred to in the game as Nerve. Nerve boosts the damage and Damage Threshold of each companion by 5% for each point of Charisma a character has. So Nerve grants a total bonus of +50% damage and damage threshold to companions with 10 Charisma and only +5% to both at 1 Charisma. A person with a starting Charisma of 1 can boost their companions nerve to the maximum by use of an Empathy Synthesizer or Intense Training, Party Time Mentats (+5), high Survival (so that alcohol adds +3 Charisma) or stacking moonshine with another type of alcohol.

This is most effective with companions that gain increases to their damage, damage threshold or attack speed (movement speed is useless with nerve) upon completion of their companion quests and less important for companions who gain items or abilities not associated with nerve. Companion nerve combines exceptionally well with Ferocious Loyalty and Spray 'n Pray, the resulting durability can keep companions alive fairly well even in hardcore mode.
 * Rose of Sharon Cassidy
 * Hand of Vengeance (15% more damage with Guns)
 * Calm Heart (+50 Hit Points)
 * Veronica Santangelo
 * Causeless Rebel (Increases Veronica's Unarmed attack rate by 30%)
 * Bonds of Steel (+4 DT)
 * Elijah's Last Words (+150% melee attack speed, 25% chance to knock down enemies)
 * Raul Tejada
 * Old Vaquero (+33% faster fire rate with revolvers and lever action firearms)
 * Lily Bowen
 * Off the Meds (Permanent stat bonuses, psychotic break at 50% health)
 * ED-E
 * Brotherhood Examination (+8 DT)
 * Followers Examination (+5 DAM, +8 DPS, +0.5% Crit Chance and +15 Crit Damage)
 * Rex
 * Rey's brain (+25 damage)
 * Lupa's brain (+10 DT)
 * Violetta's brain (+50% movement speed)

Weapons
All permanent companions' default weapons have unlimited ammunition. If you equip your follower with a better weapon, (DPS is checked) add ammunition and check its count from time to time - they seem to hold on to the new weapon when out of ammunition or switch to melee instead.
 * Companions cannot use weapon upgrades (mods). The upgrades are simply "removed" when you give a modded weapon to a follower and the weapon works in its basic way. The mods will still be on the weapon if it is removed from the follower's inventory.
 * Companions can use unique weapons with already built-in upgrades like the Ratslayer.
 * Companions can use all types of ammunition, but they seem to hold on to the particular type when you equip them with different sorts of one caliber. When out of ammunition, instead of switching to the other type of that caliber they use melee instead or sometimes get stuck in a "reload loop". To avoid this, simply give them only one sort of the same caliber.
 * Most companions wear a weapon that's named after the companion. They share the same main characteristics as the generally named weapon and only differ in name.
 * Arcade Gannon's Ripper
 * Arcade Gannon's Plasma Defender
 * Raul's magnum revolver
 * Raul's lead pipe
 * Veronica's power fist
 * Veronica's 10mm pistol
 * Boone's machete
 * Boone's scoped hunting rifle (unique)
 * Cass's caravan shotgun
 * Cass's combat knife
 * Lily's assault carbine
 * Lily's gauntlet (unique)
 * Lily's Vertibird blade (unique)

Armor
Permanent humanoid companions can wear and/or carry all types of clothing that is not associated with any faction. They can also wear all types of armor and power armor that is not related to a faction, even without having Power Armor Training. They only change gear if the given one has a better Damage Threshold than their own outfit. This may not always hold true, however; giving multiple copies of the same outfit to a companion may result in them equipping an inferior copy, despite the difference in DT.

Companions will refuse to wear or even carry faction-specific apparel, except apparel corresponding to their faction. Giving invalid faction apparel to a companion will result in that companion immediately dropping the item (see Bugs for errors that occur with this); it is not returned to the player, but must be picked up from the ground. This also applies to non-human companions who cannot wear armor, i.e. Lily Bowen, Rex, and ED-E. Only Boone and Veronica are able to carry or wear faction apparel. As a former member of NCR 1st Recon, Craig Boone will carry or wear any NCR faction apparel. Veronica, as a member of the Brotherhood of Steel, will wear Brotherhood power armor. She will also accept apparel specific to the White Glove Society, and giving her the items White Glove Society attire or Formal wear will result in her teaching you the unarmed move Scribe Counter. She will not wear these items, however, because their DT is inferior to her default clothing.

Behind the scenes
Several remaining resources point to the game having at one point allowed for the Courier to have multiple humanoid companions. Primarily this is found in disabled dialogue options, such as a conversation with Mortimer where the Courier would have needed to specify which of their human companions they were offering to Mortimer.

Bugs

 * When entering the casinos on the Strip, they will take all companions' weapons. Exiting will not return their weapons they own.
 * Arcade Gannon will sometimes not show the recruit dialogue when you have a non humanoid companion (e.g. rex or ED-E). this seems to happen when arcade is in the lucky 38. the only way to fix this is to dismiss all companions, then recruit arcade then recruit the other companion again.
 * After dismissing Arcade to the Lucky 38 and re-recruiting Boone at the same location, Boone's default weapons shifted to those of Arcade's (Plasma defender & Ripper).
 * Companions who are poisoned will have the full effect of their poison "dumped" when using a stimpak on them. This can result in negative HP which cannot be cured with more stimpaks, and they will die as soon as you exit the companion wheel. (For weaker poisons, this may lower their HP, but since it doesn't go below zero, they don't die.) On the other hand, they will not use antivenom, so the poison may end up killing them naturally. This is especially a problem with Veronica, as she prefers unarmed combat. Patched in Fallout: New Vegas patch 1.3.0.452.
 * One way to solve for it is to prevent them from being poisoned in the first place. Make sure they are set to ranged weapons before fighting dangerous poisonous creatures. (Veronica, despite her complaints about using ranged weapons, is very good at Energy Weapons.) If the fighting is really bad, just have them stay put and tank the creatures yourself. (At least you can use stimpaks and antivenom without ill effect.)
 * Another way around this includes having hardcore mode turned off (if it is active). The poison will cause your companion to go unconscious a few times, but the poison will eventually wear off. After that, hardcore mode can be turned back on. The reason for this working is simply because in casual mode, companions are set as essential and cannot die.
 * Note: Turning off hardcore mode at any point in the game will disable the hardcore achievement, so this solution is not recommended for anybody who is trying to get that achievement.
 * Yet another way is to tell the companion to wait, which appears to replenish the companion's health and remove the poisoning. The follower can then be asked to rejoin. This can be performed even during combat.
 * Temporary solution is sending your companion home or to the Lucky 38 then recruiting them again.
 * Alternatively treating them with stimpaks very quickly after they are poisoned will prevent their health becoming negative and actually heal them instead of killing them. Note that it can take 20+ stimpaks to fully heal Rex.
 * The option to dismiss companions to the Lucky 38 will disappear even before Mr. House becomes hostile to the player.
 * Items in companion inventories will sometimes disappear from the inventory, yet the weight of the item(s) will still remain.
 * Sometimes, when entering combat from a disance with a melee enemy while your companions are also set to melee and placed right behind you can result in them getting stuck on the Courier and ultimately killing him/her when they try to attack the incoming enemy.

Fixed bugs (Patch 1.2.0.31x)

 * If you have several companions in the Lucky 38 at one time and leave Weapons lying around they may start to fight each other and they will die due to the fact that they are no longer listed as an essential. A solution is recruiting the one that the other companions are ganging up on, so that they are essential. Once that companion is knocked out the fighting stops. (Sandbox-AI caused human companions to attack non-humans if the latter carried consumable goods)
 * This may be not completely fixed in player/1.20.352: There was an instance of Rex and/or EDE attacking the human companions upon returning to The Lucky 38: This only seems to have been corrected after going back a couple saves and removing all remaining inventory from Rex; see more details at Talk:Rex (Fallout: New Vegas).
 * Dismissing companions to the Lucky 38 can sometimes result in them staying in the same location instead of moving to the Lucky 38. So if you cant find your companions at the 38, check where you dismissed them. (As of Patch 1.2.0.31x companions no longer walk to their residence but are teleported immediately).
 * The achievement/trophy The Whole Gang's Here doesn't count the companions you've currently recruited, but rather the total number of times you've recruited a companion. Furthermore, this count is not restricted to a single playthrough, so it will count "repeat" recruiting of a single companion. It is thus possible to recruit the same four companions over two playthroughs and get the achievement.
 * Sometimes when entering a casino, your companion will lose their weapons, and upon leaving, they will still not have their weapons. Mysteriously, the Courier will have it. It is impossible to give it back. The guns run on MCA ammunition, so they just clog up the inventory. To fix this, tell your companion to wait outside. This can happen to ED-E.
 * When you enter any place where your weapons are taken away, your companions will often not get them back. this is extremely frustrating, especially if the companion was holding unique weapons.
 * When entering Lucky 38, Vault 21 or the Gomorrah courtyard with Veronica, she occasionally was removed from the game.

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