What is required viewing? And required for whom? Just because I found a show to be of great value, doesn't mean it's required viewing. For example, I consider Azumanga Daioh to be on of the best anime series available, but I also wouldn't consider it required viewing. Highly recommended, but not required.
Most people just want to watch what they want to watch. So I would say there is no required viewing for most, save what is in their favored genre, and that would change based on individual.
Now, if you wish to be a true otaku and reveal in all that is anime, there are certainly some titles you will want to be able to speak on, to know how anime came to be what it is today. Here, I will attempt to lay out the course to true anime geekdom, or lay out How to Impress the Elitists at Your Local Con. (Note: Not all titles are suitable viewing for all audiences. Some content is definitely not for children and may offend many adults. I, personally was very offended by Escaflowne, but that’s a story for another time
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Understanding Anime History - the trend setters:
These are all from the “early daysâ€