Out of the classics, Neon Genesis Evangelion, which has also influenced many anime
Another one would be the Legend of the Galactic Heroes but I personally enjoy it more because of the space battles, the complex politics and Yang Wenli
Rose of Versailles has a similar theme as Utena but it's not as good
Inuyasha if you just want some stuff that deals with Japanese mythology and is also fun to just sit back and watch
Then there are all the Ghibli studio movies, my personal favorite being Spirited Away.
Out of the recent anime from the last decade, though, I would recommend Madoka Magica as a starting point.
Of course there's a lot more but those are the ones that pop up immediately