Frodo/Sam. I read the book/s when I was a kid and just didn't see ships, the movies came out when I was in my early-mid teens and shipped everything that moved, and now I pretty much see them as platonic soul mates, but not romantically or sexually attracted to each other. Teenage me didn't really have much interest in non-romantic love, now I adore those relationships. It's still my favourite relationship in the series, just not... a ship.