I agree with most of the recommendations from the 90s and early 00s, so I'll name a few that haven't been listed yet.
Requiem from the Darkness is a very good horror series that leans into more classical Japanese art than standard anime.
On the exact other end of that spectrum, Code Geass is a flawed, but generally interesting political thriller mecha show.
I personally liked Blood+ when I was a teen, but I'm pretty sure it's because I
like the aria more than the show itself.
Macross Plus is quite possibly my favorite movie too, but it has to be the movie edition and not the 4 part miniseries because the score is different. The miniseries has a lot of... how do I put it... temp tracks in it. They're not precisely temp tracks since these songs did make it into the OST, but they do act as placeholders when compared to the movie version, which has songs scored for specific scenes.
Miniseries score: Break Out
Movie Edition score: Dogfight
Another example is how overused
Myung's theme is in the mini series version. It's a good song, but there's one romantic scene where
More than 3cm works better for the scene.
I haven't kept up with more recent shows. I tried Jojo's Bizarre Adventure and I just couldn't get into it. My impression is that too many shows are like Sword Art Online where it's 1) written by an Otaku and 2) is an inferior version to the .hack series anyways.