These used to be considered classics back in the day.
The 2000s are a very weird era. Anime has already moved past cel animation and started becoming digital, but the otaku fandom is still not as big as it will become later on. During this era, there were a lot of fairly unique shows that often fly under the radar of modern fans.
If you have a Crunchyroll subscription, you can watch some of them.
Natsume's Book of Friends
MyAnimeList score: 8.31
Natsume’s Book of Friends (Natsume Yuujinchou) is considered one of the perfect examples of slice-of-life that doesn’t focus on a school club. The protagonist, Takashi Natsume, feels weird and isolated because he can see all sorts of spirits — yokai.
One day, he finds the Book of Friends — which belonged to his grandmother, who had the same ability. Now, Natsume wants to befriend various spirits. Many episodes work as great stories on their own, and by now, six seasons are out — and the seventh is announced.
Skip Beat!
MyAnimeList score: 8.08
It’s strange that no one talks about Skip Beat! these days: the manga is still ongoing, and the anime was considered a classic of shoujo romance back then.
Of course, by now, the romance aspect has been explored better in other series, but there’s one thing where Skip Beat! truly shines. It’s a great portrayal of the show business industry and how cruel it might occasionally be.
Last Exile
MyAnimeList score: 7.80
Last Exile was considered one of the best sci-fi series one day. It has a very unique and detailed setting, and that alone is a good sell for sci-fi fans. It also has a fairly good story, though it can be hard to get into at first.
The anime was produced by studio Gonzo, who were famous for making these weird, semi-experimental sci-fi series during the 00s era.
MyAnimeList score: 7.62
Utawarerumono is actually a pretty popular game franchise, but the main story was also fully adapted in three seasons of anime. The story… is hard to explain, as it starts out very simple: an amnesiac man being found by a settlement of demi-humans. Then, it goes progressively more and more convoluted.
If you like fantasy series and don’t mind binging anime — watching this with multiple breaks will not do you any favors — this one might be for you.
Akagi
MyAnimeList score: 7.94
If you’re familiar with Kaiji: Ultimate Survivor (Gyakkyou Burai Kaiji: Ultimate Survivor), you probably have heard of the mangaka’s other major work. To be fair, it’s easy to guess that Akagi (Touhai Densetsu Akagi: Yami ni Maiorita Tensai) is made by the same mangaka.
Unlike Kaiji, which is an anime about gambling in different high-stake scenarios, Akagi focuses solely on mahjong. If you’re familiar with the game, this is practically a must-watch: the series is a psychological thriller where you win or you die.