So what good anime series are there? Far too many is what I'd say.
Obviously what you find good will depend on what genre you prefer - some
people like action, others sci-fi, others romance.
I would suggest you checkout Animesuki grab a popular looking series and have and explore of the forums!
Studio Ghibli (pronounced "gib-li") & Hayao Miyazaki (Hey-oh Me-a-zaaki)
Studio Ghibli is very well know it has produced many films (rarely series), and is generally considered to be one of the best studios. Miyazaki is the directory/producer as Ghibli studios and he is extremely talented. A few studio Ghibli productions:
- Spirited Away (Won an Oscar I think)
- Kiki's Delivery Service
- Princess Mononoke (I think - either way it's good)
- My Neighbour Totoro