Some currently on my mind:
Bokurano ED 2 - Vermillion (such one depressing story, much more so in the manga 
)
Bokurano OP - Uninstall
NHK Ni Youkoso ED 1 - Odoru Akachan Ningen
Steins;Gate OP - Hacking to the Gate
Dennou Coil OP - Prism
Serial Experiments Lain OP - Duvet
Ergo Proxy ED - Paranoid Android (I was like “Holy hell Radiohead for an anime ED! 
”)
Cute songs too. 
Nichijou ED - ZZZ
Danshi Koukousei no Nichijou ED - Ohisama
Anime opening/ending isn’t only about the music, but it’s also about the video overall. So I guess this thread is acceptable.
Most of my favourite openings come from One Piece, such as Believe (op2), One day (op13), Hands Up (op16), Wake Up (op17-current opening) :
My favourite endings are : Induyasha endings (My Will, Fukai Mori, etc), Death Parade ending (Last Theatre), Arslan Senki ending (Lapis Lazuri), Gundam Seed endings (Toki no Sabaku, etc), Samurai X ending (Heart of Sword).
who kill my dad!!!
Currently watching the Jojo anime and I thought the ending (and anime) was surprisingly awesome.
And kinda a lesser known anime that I found from late night syfy channel watching.
Here some of the openings I like
Gurren lagann
Sword art online season 1
Guilty crown
Bakemonogatari Fourth opening
Death Note opening 2
I have a thousand more but i don’t want to post them all
Plastic Memories Ending
Gunslinger Stratos Cover Ending
Feels :C
Nobody posted this yet?
I’ll post here some of the the best openings and endings in my opinion
Wolf’s Rain OP
Basilisk OP
Speed Grapher OP
Shakugan no Shana ED
https://youtu.be/706WX21dCBY
Katanagatari OP
Kurozuka ED
Tasogare Otome x Amnesia OP
Slam Dunk. Up to date, still my all time favourite. Used to watch it myself at the age when I could still play basketball. In a way, it was inspirational.
Kids these days judge each other by their tastes in anime…
god I feel old
Best Anime Op ever…
more op… when the now comercial jpop wasnt that mandatory…
epic stuff…
is a game but still work…
another game…
note the second from right one… XD
dango…
a good op isent about a catchy song…it have to be all… animation… music…sincro…simbology…etc etc… like this one…XD
or this one… perfect ed for a series…
of course there are hundreds of good anime ops and eds… but only a few ones really are artistically diferent… like this one XD
So cute