Has Hayao Miyazaki ever made an anime series or manga? Hayao Miyazaki is a famous director of anime movies such as "Spirited Away" and "My Neighbor Totoro".

But has he ever made any anime series or manga besides movies? If so, what are they?
Miyazaki is surprisingly prolific as a creator of manga. His best-known work in the medium is, of course, Nausicaä of the Valley of the Wind, on which his movie of the same name was based (for an interesting comparison of the different versions, see here). In a similar vein, he created a short manga for The Wind Rises a few years ago, in the leadup to the film. You can check out his Wikipedia article for more details. Reports suggest that Miyazaki is currently working on another manga, which will apparently be about samurai. 

Miyazaki has never been the sole director of a television anime, but prior to his work on Nausicaä, he did extensive work on a number of television anime series (animation at first, and later, episode direction and co-direction), first at Toei, and later at A Pro and Nippon Animation (after that, of course, he founded Ghibli, and the rest is history). Prominent works in his oeuvre includes the first Lupin III anime and Heidi: Girl of the Alps (both co-directed with long-time collaborator and Ghibli co-founder Isao Takahata). Since Nausicaä, however, Miyazaki has done no further work on television anime. 

Note: I forgot about Future Boy Conan, which is basically a Miyazaki show, technicalities of crediting notwithstanding (thanks, @JonathanVanMatre). For more details, take a look at @leonbloy's answer.