My favorite intro is Made in Abyss Season 1. It's so beautifully animated, colorful, and epic. It really excites you on this adventure. I also love the music, it's awesome! The voice actresses themselves are singing as the characters! How cool is that?
My favorite outro is Little Witch Academia Season 1 (technically it's the same season in Japan but still). It's beautiful as well, and the little animation transition thingy is so fluid and nice to look. I love the little drawings showing the characters going on little adventures we never got to see in the show proper. My favorite is the one with Akko, Lotte and Sucy on the roof having a picnic, it's very charming. The music is pretty neat as well. Honestly I'm a little disappointed by Season 2's outro in comparison. It's way more minimalist and while the animation is fluid, it doesn't really stick in your mind as the first one. Also I find the music to be more generic idk.