The bands The Pogues and Violent Femmes and considered the founders of the genre.
The record label, Plan It X Records, a label based out of Bloomington, Indiana, is primarily responsible for making the sound popular in America. Other prominent folk punk labels include Fistolo Records out of Philadelphia and Riot-Folk! Records, which is very loosely based out of Maine (you'll have to check the website to understand what I mean, in fact, I might end up doing a post just on this place.
Bands in this genre tend to use "traditional" instruments such as violins, banjos, mandolins, and acoustic guitars rather than its electric counterpart.
From what I have been able to tell from my reading about the genre is that the bands in this genre are, in general, strict adherents to the DIY ethic of doing business.
Some bands/artists that are considered to be part of this genre/movement are:
Andrew Jackson Jihad
Started in 2004 in Phoenix, AZ. They have released 4 LPs, 5 EPs, and have been on several splits and compilations. They have been on the Plan-It-X and Asian Man record labels. It is comprised of Sean Bonnette and Ben Gallaty.
This band began in Columbus Ohio (not Defiance) in 2002. It has been affiliated with Plan-It-X Records, No Idea Records, Anti-Creative Records, and Friends and Relatives Records. They have released 4 LPs, 3 EPs, and have been featured on 3 splits.
The Can Kickers
Based out of Connecticut, The Can Kickers were formed in 2002 and are comprised of Doug Schaefer, Daniel Spurr, and Daniel Thompson. This band's instruments of choice include, banjos, washboards, fiddle and the mouth organ.
They have released 5 albums, including a live album. They considers themselves to be "what would happen if Minor Threat and The Ramones picked up banjos and fiddles..." and are a cross between punk, folk and zydeco music.
Political activist Billy Bragg was born in 1957 in England and originally began performing in 1977 with the punk rock band Riff Raff. As a solo artist he has released numerous albums and has been the labels Charisma, Go Discs, Elektra, Liberation Records, Strange Fruit, Cooking Vinyl, and ANTI-Shock, among others. I'm not really sure if his affiliation with Elektra Records classifies him as folk-punk in my book considering signing with a major label kind of goes against the DIY idea that I have of the genre/movement but considering the guy has been doing it for several decades, I'll give him props here.
I did a Discography of the Moment here on Otter Limits of this guy yesterday. I also put some videos of his work on here as well yesterday. Most of his work has been independently released. About as close as he has gotten to signing with a major label is his affiliation with Epitaph Records.
An Introduction to Folk Punk on Razorcake, a non-profit website devoted to supporting indenpendent music.
List of Folk Punk Bands at Ranker.com, a website devoted to lists. (I found this website randomly while looking up material for this post and can't help but think, hey, this is my kind of website!)
Folk Punk Facebook page.
Folk Punk Wiki article.