Party Limit

Under the SPECIAL system, players are limited to a certain number of non-player character (NPC) followers in their group. This limit is called a party limit. The number of NPCs following a character at a given time is usually referred to as the party count.

Fallout
The number of followers you can have in Fallout is not limited, other than by the total number of available followers in the game.

Fallout 2
The party limit in Fallout 2 is a derived statistic based on the character's Charisma SPECIAL stat. The party limit is calculated thus:
 * Limit = CHARISMA / 2

When the charisma stat is an odd number, the result is rounded down. Ergo, a character with CH 9 will only be allowed 4 NPCs. Since SPECIAL imposes a strict cap of 10 on all stats, a player can have, at most, five "normal" NPC followers.

Exceptions to party limit rules
Some NPCs are immune from the party limit rules based on their scripting. These NPCs are programmed differently from other follower NPCs, and are therefore subject to their own conditional rules, separate from the party limit rules. In these cases, the addition and removal of these NPCs from the party is typically dictated by set triggers rather than dialogue.

Laddie
Laddie, the dog from Modoc, is automatically added to the party when the player undertakes the quest to find Jonny. If the player is below the party limit, Laddie counts as a follower NPC. However, if the player is at the party limit, Laddie is still joined to the player's party regardless. The NPC is not detached from the party until the quest conditions are fulfilled, and as such cannot be dismissed like another follower.

The Pariah Dog
The special encounter Pariah Dog is another limit-exempt NPC. In this case, the dog is automatically attached to the player's party whether or not the player is at the limit. If the player's party is not full, the dog is attached and counts against the party limit in terms of recruiting other NPCs. If the player is at the party limit, the Pariah is still attached to the player's party and counts as a follower, meaning that unless the dog is killed, the player will not be able to recruit a new follower until the player's party is back below the limit.

Calculating In Limit-Exempt NPCs
If a player has a Charisma score of four, then that player can have two NPCs as followers (CH4 / 2 = 2). For the purposes of this illustration, the player has two followers, Marcus and Cassidy, meaning the player's party count is two. The party is at its limit. If the player comes across the Pariah special encounter, the dog is attached to the player's party. As the Pariah is treated as a follower NPC, the player's party is now over the limit (3 out of 2), but the rules programmed into Pariah override the party limit and insert the dog into the party. If the player wanted to recruit, for example, Vic, the player would have to fire both Marcus and Cassidy to get the party below the limit; firing both reduces the party count to 1 (Pariah), enabling the recruitment of a new NPC.

Fallout 3
Aside from glitches and modifications, it is only possible to have one permanent non-Dogmeat type companion, as well as Dogmeat himself, in your party. An unlimited number of temporary type companions can be added in addition to Dogmeat and the permanent companion.

Fallout: New Vegas
Overall the same rules apply from Fallout 3, you can have 1 humanoid companion, and 1 "animal" companion. The main difference from Fallout 3, is that during normal mode companions will not die, but can only be rendered unconscious. In hardcore mode, normal rules of death applies. However, it is possible in normal mode for your humanoid companions to die, as in this example:

After you've had Boone for a certain amount of time, you can initiate dialogue (through the companion wheel) and get him to open up about his wife. Once that is finished he can die. (In his inventory (specifically when he's dead) you may find a special item on him.)