In Fallout 2, Charisma also determines the number of base companion slots the player character is given. This number is equal to their Charisma score divided by two, rounded down. For example, if the player character has a five Charisma, they can recruit two followers. Please note that the player character can still recruit one follower even with a Charisma as low as one.
Predesigned Primary Charisma-based Characters (PPCC) of Fallout are Albert, and in Fallout 2's case, Chitsa.
In Fallout Tactics, Charisma is, at best, a secondary trait. Due to the nature of the game (i.e. almost exclusively combat-based) it is feasible to complete the game easily with 1 or 2 Charisma with no penalty. The only role is that when the Warrior starts with Charisma of 10, his/her rank is Senior Initiate, rather than Initiate. It is involved with the Barter skill and promotions, and is required for the Leader and Divine Favor perks. A low Charisma, on the other hand, gives access to the Loner perk.
Charisma increases the disposition of all NPCs, which makes Speech checks easier. Disposition is also affected somewhat by Karma (most NPCs like good characters more), quests (doing a quest in a way an NPC likes can dramatically boost disposition), and dialog options (being a jerk in conversations can lower disposition a little). Charisma also affects the Barter and Speech skills. Characters who use Speech will want at least a decent Charisma, but adding points to the skill is almost always better than adding points to the score. Characters who do not use the Speech skill have little use for this SPECIAL score.
There are also general Charisma checks in dialogue with some characters, in addition to Speech checks. Avoid wearing things like Enclave Power Helmets, as they deduct 1 point of Charisma while equipped.
Charisma in New Vegas modifies Barter, Speech and Companion Nerve. Companion Nerve gives each companion in the party +5% to their damage and armor, up to a maximum of +50% at 10 Charisma.
Regardless of Barter or Speech level, some interactions will not be available if your Charisma is too low (Ex. Corporal Betsy). These ultimately do not have any significant effect on game play, nor do they provide any special bonuses.
If the player's Charisma stat is the most extreme (highest or lowest), Doc Mitchell will either say "Good to see them bullets didn't affect your charm none." (for highest) or "Huh. Must be some frontal lobe damage." (For lowest)
It's worth noting that temporary Charisma boosts like alcohol do NOT count towards the maximum amount of companions calculation; if the player is at an odd number like 5, temporarily boosting Charisma will not allow them to recruit another companion if the previous slots are already taken.