Classy 1978 anime series by Hayao Miyazaki that is available fansubbed. So of course like the idiot that I am, I've not seen it.
It's based on the novel The Incredible Tide by Alexander Key. A magnetic weapon has disrupted the Earth's axis, flooding the world. Conan lives on an island populated by the survivors of a failed bid to escape Earth to the stars.
It's only 26 episodes long so I suppose I really ought to download and watch it.