Well you've got (ones I can remember), i'm not going to bother with NV ones, theres a list right already in the thread and there's to damn many
The Crimson Caravan
The water merchants
The Master's army
Butch's caravan company which I can't remember the name of
The blades
The Regulators (FO1 and FO3 variants)
Gun Runners
Talon Company
Slavers (FO2 and FO3 variants)
Raiders FO3 style (not 100% sure about this one)
Khans
Vipers
Jackals
NCR rangers
Children of the Atom
The hubologists
The families of Reno
Shi
Reily's Rangers
plus the ones you stated
There are more I just can't remember them all, some play not so big roles and others are pretty important
To me a faction would be a group of people who has cohesion and leadership and 'chain of command' hence why i'm iffy about FO3 raiders being a faction
edit: nearly forgot one of the most important faction in FO1, the Children of the cathedral