to the beginning from Fate/Zero (EDIT: I originally said "both OPs" but I got mixed up with one of the EDs -- the other OP is oath sign performed by LiSA)
the Ghost in the Shell SAC OPs -- particularly Rise fron 2nd Gig
I usually watch an OP once for a show and then skip it each time afterwards. That being said, there are a handful that I remember making the choice to always watch each episode. In no particular order:
Conan during the who is bourbon arc. I was pumped during that arc. I skip 90% of episodes not based on the manga so it only played for like 6 eps or so.
Psycho pass, all. Even the one I initially didn't like got an animation change which somehow saved it.
Preserved roses. Actually almost any tm rev or Abingdon boys school. It might have been an ending but the Tokyo magnitude 8 Kimi no uta. Darker than black, several Gundam and similar, etc.
The opening of beastars has amazong animation and some kinda silly vocal maneuvers that all together I liked more than the whole anime.
One or two from the old Inuyasha that went for like 509 episodes and didn't even finish the main plot.
Several themes from steins gate game and anime. They always bring back the feels.
The entire sound track of natsume yuujinchou. That also gives me nostalgia hits.
Aku no hana. The anime was strange to say the least but that song really layered on the stress.
All the kalafina songs in fate/¿? I think /zero. I really like kajiura's music. Heavenly blue used in aldnoah zero too. The lyrics are really nice and fit the show really well.
Probably tons more. Like one for every 5 bad ones though.
I thought my answer would be Ghost in the Shell Stand Alone Complex, because the theme song is so good. However I just rewatched it, and it's full-on early 2000's bad 3DCG.
My actual favorite overall has to be One Punch Man then.
It may not be my favourite but the english dubs of the early one piece openings and endings make me tear up with nostalgia. I haven't even followed the anime since many years
Another I remembered and wished I'd mentioned - Azumanga Daioh
It's so obviously a nod to Sparks, which is fitting for such a surreally goofy anime. And that's a neat bit of recursion in itself, since Russell Mael at least (and possibly Ron too) is an otaku. I've never seen anything official about their influence on the song, much less about their reaction to it, but I like to think they were flattered.
I have a huge nostalgia shaped soft spot for the early One Piece openings.
I really like "Lay Your Hands on Me", the opening for Kiznaiver, despite the anime itself being a huge disappointment.
Death Parade's "Flyers" is a masterpiece.
Others that come to Mind:
ACCA 13
BNA
Flip Flappers
Made in Abyss
OPM
Steins Gate
Trigun Stampede
I legit can't choose. There's some really good stuff out there. In terms of what I've listened to the most, that's likely Shout and Gravity Wall, the OPs of Re:Creators. The story is kinda meh, but man does that show has some high highs, and the OPs are one of those.