Anime

Frieren's ED is phenomenal, no arguments there. Probably one of my favorite EDs of all time. Others that come to mind for me would be:

• Hana no Tou - Lycoris Recoil
• Hikari e - Zombieland Saga
• Chiisana Boukensha - Konosuba
• Chiisana Koi no Uta - Karakai Jouzu no Takagi-san (I haven't watched this series, but this is an incredibly famous song and this is one of my favorite versions)

secret base ～君がくれたもの～」B ver. from AnoHana - because it makes me instantly relive all the emotions felt while watching the anime.

Sore wa Chiisana Hikari no Youna from ERASED - same reason as above.

Dango Daikazuko from CLANNAD - same reason as above.

Tabi no Hidarite, Saihate no Migite from Made in Abyss - sounds like such a fun series, right? Right?! But yeah, I unironically like that song and sing along in the car. Trying to not “same reason as above”.

Okami Blues from Seton Academy - another depressing sing along song that’s actually depressing.

Maid no Komoriuta from Akiba Maid Wars - because it’s hilarious.

Gotta Knock A Little Harder from the Cowboy Bebop Movie - because it’s my favorite song in general.

Kuroi Namida 4th ending from NANA - and we’re back to the depressing shit. Might have a problem.

Although I enjoy songs mainly because they sound good to me (usually because they are catchy / pop-rocky), there are some endings that stood out to me beyond just their audio:

Comedy a.k.a. Kigeki by Hoshino Gen (Spy x Family)

• The visuals is essentially Anya's dream. I especially like the latter part, of them having happy, heart-warming family time.

Sweet Sign by Misaki Nako (100 Girlfriends)

• The visuals show a small, self-contained story, and showcased the essence of the girls' relationship with each other.

Kimi wa Boku Niteiru by See-Saw (Gundam SEED Destiny)

• Whenever something sad happened in the show, this ending song starts playing, elevating the feeling of sadness.

unlasting by LiSA (SAO: Alicization - War of Underworld)

• Looks like major spoilers.

My Nonfiction by Kaguya-sama cast (Kaguya-sama season 3)

• It tends to get overshadowed by the Chika dance, but this ending does everything well: great audio, great visuals (with the change in art style), and most of all, it's the perfect follow-up to the episode.

What's an ED?

Odoru Akachan Ningen from NHK ni Youkoso!

I can't find the ED itself but I really love the energy in this song.

I love EDs that tell a story!

My favorite one of those is the original Babel II ED from 1973

Along with a classic song by the late great Ichiro Mizuki, it also portrays the henchmen as dangerous, even though our hero manages to defeat them anyway.

A more recent one is Paripi Koumei/Ya Boy Kongming's ED

Another fantastic song from this series by 96NEKO. The story in the ED is an idealized version of the story with SD versions of the characters

Again, going back to the 70s, 1974's Majokko Megu-chan ED

The song by the great Yoko Maekawa isn't the greatest, but the care in the animation and background art is far greater than typical TV anime art for that era. The little dog is very cute, but I don't think it appears in the actual story in the show.

Michishirube by Chihara Minori from Violet Evergarden

Koko kara, koko kara by Tamaki Mari (CV: Minase Inori), Kobuchizawa Shirase (CV: Hanazawa Kana), Shiraishi Yuzuki (CV: Hayami Saori), Hinata Miyake (CV: Iguchi Yuuka) from A Place Further Than The Universe

Que será será by fhána from Uchouten Kazoku 2

Kimi to nakushimono by Kitazawa Ayaka from Little Busters! Refrain

Mata kimi ni aeru hi by Miyawaki Shion from Ansatsu Kyoushitsu season 2

Utsukushiki Zankoku na Sekai by Yoko Hikasa - Attack on Titan ED1. The melody is a startling contrast from the anime itself. Unlike the action packed and destructive anime, the song is gentle and pure, sad and foreboding, but with a measure of strength. Like someone (namely Mikasa, featured in the video) desperately fighting to hold on to something that will inevitably escape their grasp.

ED from Keep Your Hands Off Eizouken! more for the music than visuals.

As mentioned in this thread Song of Raindrops and Koko kara, Koko kara are also good

• Sora wa Takaku Kaze wa Utau from Fate/Zero (2nd cour) -- it's a powerful song, and I think I listened to this one all the way through in every episode. Definitely one of my all time favorites.
• Taiyou - Denpa-Teki na Kanojo. (This OVA is pretty obscure, I think.) Another powerful song. No visuals for most of the ending (just text credits scrolling) -- although 神戸守 (Mamoru Kanbe) listed as the director (監督) jumped out at me! No Klimt this time, but funny that I'm talking about something he worked on again already. Maybe I should go track down his other works more systematically...
• Kesenai Tsumi - FMA 2003 -- I have a lot of nostalgia for this song and listened to it way too much as a teenager after my friends started introducing me to anime. The version on animethemes is a bit different from what I remember visually but the song is the same.
• Wareta Ringo - Shin Sekai Yori -- I was actually thinking about posting an animepic clipped from this the other day since it popped back into my mind...
• Hibari - Lord El-Melloi II Sei no Jikenbo: Rail Zeppelin Grace Note (the Fate/Zero spin-off series) -- I like both the song and the visuals (with the seasons changing)
• My Pace -- Bleach ED6; I didn't much care for the filler seasons of Bleach, but the synth from this ED and the dancing characters got stuck in my head for a while.
• X Jigen e Youkoso - Space Dandy. This one is memorable to me both for the "Hey, Everett..."/「ねぇ、エヴェレット」bit specifically and the general subject of the song.
• Zzz - Nichijou -- both the art and song are great. There's a couple versions, but I like this first one the best.

Edit: corrected the link to the Space Dandy ED

Torikago, from darling in the franxx is one of my favorites. It's definitely also an emotional one