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This is inspired by http://blogofholding.com/?p=6992 but grew quite a bit from that list. It generates factions and other major influences within a village, town, or city (you can specify, it just affects the number of influences) which might be competing forces, or the most powerful force in each of several neighborhoods or quarters.
Two major influences in the town are lawless exiles who make up nearly the entire population of the settlement and a manipulative seer who knows too much about everyone.
The major influence in the town is a school for combat instruction. Other influences are the commander of the local militia and a lasting magical effect which summons or draws particular creatures.
The major influence in the town is a cult with extensive membership. Other influences are a rich business owner (e.g. of a lumberyard, mine, etc) and a lasting magical effect which prevents entering/leaving under certain conditions.
Two major influences in the town are a rich landowner and a wise seer.
The major influence in the town is a powerful monster who demands sacrifices.
The major influence in the town is a well-respected elder. Other influences are a reckless and dangerous mage and recurring appearances of minor monsters that the residents have learned to avoid.
The major influence in the town is an extremely fashionable group of high-status individuals. A secondary influence is a mercenary band.