Almost exclusively based on manga, their print equivalent, anime stretch in a plethora of genres, address audiences of all age, sex, and preferences, and entail elaborate animation, despite being in their majority, at least partially hand-drawn. Here is a list with some of the best series in the category.
Just a few notes though. Each title represents the whole franchise, for example, the Monogatari title, includes Bakemonogatari, Nisemonogatari, the Evangelion one the remake etc. The descriptions and videos of those titles will be paradigms of the whole franchise. The list does not include films, just series.