Girl that Leapt Through Time is a good one, and that's why everyone's recommending it.
Grave of the Fireflies. Sad, depressing, kids dieing, but a very powerful movie.
BlueSeed is an anime series about nature vs humanity with Japanese folklore themes. 26 eps, very fun to watch (I loved it dubbed outside of Momiji. And subbed was pretty boring without Sakura (who's dialogue is hilarious)).
If you haven't, you should marathon Mushi-shi. Very folklore as a whole, each episode is separate from the next, and it has a Very Ghibli-esque feel. A slew of stories about people having to deal with spirits (elemental and spiritual, usually small), but the spirits are part of nature - and the main character, a 'Mushi Master' has to help them all come to terms with their problems.
Hunter X Hunter is another series about a boy who aspires to become a hunter to find his father. More ghibli-esque in the sense that it's a fun kid's anime with characters you can really connect with... That and Gon's knowledge is that of nature and fishing. There are Four volumes and an OVA or two that continues off of that (OVA you can only find fan-subbed).
Ah! My Goddess is an extremely cute anime about a guy who decides to make a goddess his girlfriend. The first OVA is about 6 episodes long and has a very full-filling story. That's if you enjoy the fact that Ghibli movies tie into strong female characters.
I don't know if it counts as anime, but you should see Titan AE at least once in your life. Great movie. Space-themed... But oh so awesome.
And my mind has petered out on suggestions I can give off-hand. If you enjoyed those animes, feel free to ask for more from me.