I wear brown ties with my navy suits all the time. I think the colors look amazing together. (i can't think of a time when it wouldn't be ok for business use, unless you are thing to a formal event) I wouldn't wear it to an interview though.
For the record i have two solid navy suits, a flannel navy pinstripe three piece, and a solid navy flannel suit. Brown ties and green are my favorite to wear with my navy suits.