Well, cem_eesti is kinda right about Estonian folk, it can be quite boring, although there also are some very nice tunes. The problem is I have no idea, where to find real Estonian folk songs on the internet. One day I hope to buy the Anthology of Estonian Traditional Music (it's kind of expensive), then I'll give you some listening examples. 
But then there are also the bands mixing folk tunes with other music. Neiokõsõ is one example, although I don't like them that much, they're nice for pop, but they're still pop. There are some nice folk rock bands I could suggest like Oort (couldn't find any samples on their page) and Tulli Lum (they seem to have samples). The singer of Tulli Lum is actually not estonian, she's livonian and also sings in livonian. Livonian is an almost dead language (only around 10 people have learned it as their mother-tongue) in Latvia and it is very closely related to estonian.
Then you ca also check the page of the Viljandi Folk Music Festival , they have a video archive of the festival (not all artists are estonian).
But then there are also the bands mixing folk tunes with other music. Neiokõsõ is one example, although I don't like them that much, they're nice for pop, but they're still pop. There are some nice folk rock bands I could suggest like Oort (couldn't find any samples on their page) and Tulli Lum (they seem to have samples). The singer of Tulli Lum is actually not estonian, she's livonian and also sings in livonian. Livonian is an almost dead language (only around 10 people have learned it as their mother-tongue) in Latvia and it is very closely related to estonian.
Then you ca also check the page of the Viljandi Folk Music Festival , they have a video archive of the festival (not all artists are estonian).
