Most of my exposure with anime was whatever was on Toonami and Adult Swim in the 2000s. I've not watched stuff like, Ghost In The Shell, Cowboy Bebop (only disjointed episodes out of order), Neon Genesis Evangelion, which I know are highly regarded.
I've seen just about every Miyazaki movie at this point. I've seen Akeria.
I'm sure there's more mainstream shows and non mainstream shows that I'm missing and would enjoy.
Thoughts?
Hajime no Ippo (english name: Fighting Spirit) is probably my favorite anime of all time. It's about a kid who becomes a pro boxer, and while it is a pretty stereotypical sports show, every single element of the show is absolutely top quality. The manga is still ongoing (I think?) but there's no filler because whenever they caught up to it they stopped producing episodes and waited however many years it took for a couple more story arcs to build up - which means that the anime was released in 2000, 2009 and 2013, meaning it actually spans over a decade.
Can confirm Ippo is still going. There's been some really good chapters in the past 6 months.