Finntroll is one of the most well-known Folk Metal bands, and by well-known, I mean people who frequent online Metal forums have heard of them. Anyway, part of the band's appeal to me is that the lyrics are in Swedish, even though the band is from (big surprise) Finland. As for Folk Metal's appeal to me in general; there is something delightfully fun about having bouncy folky elements with metal music. I own three Finntroll albums: Nattfödd, Visor om Slutet, and Ur Jordens Djup. I suggest beginners try Nattfödd; it has a more upbeat, melodic sound. Visor om Slutet is mostly ambient, but also contains two of my favorite (acoustic) Finntroll songs, "Försvinn Du Som Lyser" and "Svart Djup", the latter which always gives me goosebumps. The fact that I have decent idea of what the song is about makes it that much more haunting. Ur Jordens Djup is a bit darker sounding, drawing back more to the band's Black Metal roots, while still retaining the folkiness.
"Nedgång" Video from the album Ur Jordens Djup, with the band's new vocalist.
"Trollhammaren" from Nattfödd(couldn't embed)
Månegarm + Två Fisk och en Fläsk
Another well-known Scandinavian Folk Metal band is Månegarm from Sweden. I know this band mainly through their "neo-folk" album, Urminnes Hävd (The Forest Sessions). The album is under 30 minutes long, but it is a treat all the way through.
Here you can find an mp3 from the album, along with lyrics
"Sigrblot," a sampling of the band's usual style
Researching the album a bit more led me to the group that calibrated with Månegarm, Två Fisk och en Fläsk. The groups are apparently linked by the violinist, Janne Liljeqvist. Två Fisk och en Fläsk's website is full of mp3s from their albums. I suggest checking out these songs in particular:
Två Fisk och en Fläsk's Website (Under "MUSIC")
From TVÅ FISK + EN FLÄSK
Mit Ganczem Willen
Jungfrun I Buren
From Flesh Workshop