Party Limit

Under the SPECIAL system, player characters are limited to a certain number of non-player character (NPC) companions in their group. This restriction is called the 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 a player character 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
 * $$\text{Limit}=\text{Charisma}/2$$, rounded down.

Ergo, a character with CH 9 can have four followers. Since SPECIAL imposes a cap of 10 on all stats, the Chosen One can have at most five regular companions.

Exceptions
Some NPCs can join regardless of the party limit. Usually, these are unwanted or temporary companions. They still count towards party count (i.e., with them, it may go above the party limit) and prevent recruiting regular companions until there's room. Additionally, these followers cannot be dismissed in the traditional way, as elaborated below. The exceptions are as follows:


 * Spouses (Miria or Davin); only leaves party if killed, divorced, or sold into slavery.
 * Laddie, the dog, for the duration of the quest to find Jonny.
 * Pariah Dog; only leaves party if killed.

Fallout 3
Aside from glitches and modifications, the Lone Wanderer can only have one permanent non-Dogmeat-type companion, as well as Dogmeat himself, as company. 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 are carried over from Fallout 3, as the Courier can have only one humanoid companion and one "animal" companion, the latter referring to Rex and ED-E. The main difference from Fallout 3 is companions cannot die when playing in Casual mode. Instead, companions can be only rendered unconscious. However, in hardcore mode, normal rules of death apply with a few exceptions.

Fallout 4
In Fallout 4, only one companion can follow the Sole Survivor at a time.