>>108044 (OP)It's a bad/problematic question without the asker defining clearly what he means. When the question is asked the way you asked it, people answer based on their idea about what the word means and usually they only have one single very narrow idea in their minds about what deep is and don't consider that things can be deep in many different ways. And making it worse, skewing things further, many will answer with some personal favorite anime (merely because it's their personal favorite) that happens to somewhat meet their personal conception of what deep is, and the worst about that is often their favorite is their favorite not because of whatever deep elements it contains but because of entirely different things (things that might be rather superficial) and also their personal conception of what deep is might itself be rather simplistic or childish. Thus you usually get rather dumb and highly subjective/personal replies, and also answerers fighting each other – because for instance someone might think "for something to be deep it has to have lots of mysterious/obscure symbolism that's hard to decode and never explicitly tell the audience what's going on" and if an anime doesn't have that, then they think it's not deep.
<deep spaceThe following answer therefore consists of animes that are deep in various different ways. It takes the aforementioned into account, recognizing that fictional stories can be deep in differing ways. And because OP didn't define deep, the only truly proper way to answer is with various different kinds of deep.
<deep spaceHere are some that are deep in various different ways:
https://anidb.net/anime/890https://anidb.net/anime/61https://anidb.net/anime/484https://anidb.net/anime/584https://anidb.net/anime/271https://anidb.net/anime/318https://anidb.net/anime/83https://anidb.net/anime/154https://anidb.net/anime/575<deep spaceAnd "different ways" must really be underscored; they are deep in different ways from each other, some in very different ways; 318's deepness for example is of an entirely different kind than 584's.