Secondhand Lions isn't explicitly anarchist, but it's a superb coming-of-age story with elements of personal integrity and responsibility
The Princess Bride is pretty damned anarchistic.
The Outlaw Josey Wales and a number of other westerns are fairly anti-State, too, when they demonstrate the brutality of military action.
It's been a long time since I've watched The Princess Bride. Time for another viewing I guess!
I haven't seen The Outlaw Josie Wales or Second Hand Lions but the latter is on my DVD shelf (from my wife's collection).
Thanks for your suggestions!