My suggestion, Princess Mononoke. It has a great story with some good action scenes if you like the fantasy type of stuff. Oh yeah, it's dubbed well IMO, so you can watch it in English if you prefer without it being butchered. The link has more info on the story, so check that to see if you would be interested.
And as stated before OP, if you could add in what genre you are looking for, it would help with the suggesting a lot. I'll be glad to add more when/if you get that posted.