This style has been very popular in Japan for a long time, and recently getting a lot of supporters in the West too! In Japan the natural world is highly respected, so there's not so much stigma of being a 'girl of the forest'.
I think the appeal is a soft purity, and a look of intelligence :)
Japanese shops shipping abroad
Favorite One - In my opinion, the best place to go for Mori style. Affordable, natural and lovely.
Onepi-c - lots of unique pieces, very good shop.
Ahaaha - simple, natural.
Japanese shops (require shopping service)
Lowry's Farm - Popular natural style brand.
Olive des Olive - Mid price cute Japanese brand.
Chinese shops (require shopping service)
Dear Li on Taobao - very sweet Chinese shop selling clothes and accessories.
Forest Girl Fans on Taobao - Taobao shop- I use this shop a lot, review coming soon!
If you need a shopping service for Taobao, I recommend Yoybuy, you can use my affiliate link to support my blog while shopping. Click the yoybuy icon to the right!
Muji - Actually a Japanese store but has shops worldwide. Good source of cotton basics and lovely layering pieces.
Cath Kidston - UK brand popular with Japanese Mori girls. Also has US and EU sites.
Accessorize - UK brand selling lots of vintage style and lovely lace accessories. Has branches all over the world, including Harajuku, but I think it's cheaper to buy direct from the UK shop perhaps?
Your local shops
This is probably obvious, but there are many good things to be found at local thrift shops! Mori is all about layering and texture, so while a piece may look very boring by itself, once layered it could work well :)