There's a lot of free notation out there to be found, especially for folk music. Here's a couple resources (more than enough to start with), I'm sure if I dig through my bookmarks I have a billion more, but at some point I do have to sleep. I just wanted to get the ball rolling - I'll edit more in soon!
Musescore - I've had some good luck finding arrangements of things on musescore (a digital notation software which has an online community where people post their arrangements.
Free Scores - Literally TONS of copyright-free music - classical, folk, etc.
ABC Notation - ABC Notation is one of the earliest forms of digital notation for music - it's a way to represent music using text and symbols (hence, ABC) and it can easily be fed into a generator to be displayed as standard notation or even played as a MIDI, transposed easily, etc. It was created for folk tunes, so there's a LOT of folk music on this site, and way more elsewhere on the web. I learned a lot of traditional Israeli debka tunes here, haha.
Carmine Guida - A pretty good sheet music resource for popular belly dance tunes. All the songs have the key, makaam, and applicable rhythms listed. Most have a PDF with sheet music (and lyrics), and some have a link to a video.
International Folk Dancers of Ottowa - Lots of ABC notated tunes from different folk traditions.
Dunav - An Israeli site indexing videos and music of Balkan dances. There's an option to search only dances that have the music scored.
Folkloretanznoten - One has to admire the German ability to turn any phrase like "folkloric dance notation" into one word. This site has sheet music broken up by culture of origin - there's tons and tons of Turkish music.
Trillian.MIT.edu - Another great source for ABC music, especially folk tunes.
W&M Middle Eastern Music - Lucky for us, a bunch of students at William and Mary are notating and posting middle eastern folk tunes.
Oud for Guitarists - Links to a bunch of Turkish, Arabic, Armenian, and Persian music notated. Some of the links are free, some are paid sheet music sites.