Anime

There's no way I can pick just one.

Dive in the Sky (Planetes)

Tank! (Cowboy Bebop)

Macross (Super Dimensional Fortress Macross)

Stein's Gate's OP with the song Hacking to the Gate is probably my favorite overall including both visuals and the song itself.

Prior to watching Stein's Gate my favorite was Shakugan no Shana's first OP with the song Scarlet Color Sky.

I also really liked the OP for Mahou Tsukai ni Taisetsu na Koto (Someday's Dreamer) with the song Kaze no Hana which was my favorite OP before that.

Honorable mention to Honey and Clover for having the most WTF OP out of all the anime I have ever seen.

If you're looking for something else to listen to, basically any OP by Yoko Kanno or performed by Kalafina is good. e.g.:

• Hikari no Senritsu from Sora no Woto
• Tank! from Cowboy Bebob
• 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

A few others that I enjoyed are:

• Asterisk -- Bleach's first OP
• Only My Railgun -- A Certain Scientific Railgun
• Choir Jail -- Dusk Maiden of Amnesia

but there are way too many to list, so I'm going to stop there before I write a novel.

Edit: Added links. Thanks @Davel23 -- I've been trying to stay off of YouTube lately and didn't know about that site until you posted your comment!

the Samurai Champloo opening theme is hot.

Evangelion - The Cruel Angel's Thesis

Nichijou.

Posts question to op as op and doesnt answer. Leaves

Probably Serial Experiments Lain. Duvet by Boa.

I will never skip the opening (song: Tombi) of Trigun Stampede. It made me a fan of Kvi Baba, who I'd never discovered before.

The tone and lyrics make it the perfect Vash theme song.

Pani Poni Dash! - Kiiroi Bakansu

Honorable mention - Galaxy Angel - Bang! Bang!

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:

• (NSFW) B Chiku Sentai SOX - "SHIMONETA: A Boring World Where the Concept of Dirty Jokes Doesn’t Exist" - I always laughed at the visuals of this more than anything. This show was wild.
• Onegai Muscle - "How Heavy Are The Dumbbells You Lift?"
• Idol - "Oshi no Ko"
• Zeitaku na Saji - "Campfire Cooking in Another World with my Absurd Skill"
• GO!!! - "Naruto"

We Are ! (One Piece)

Hero's Come Back from Naruto Shippuden

Honorable mentions:

• SAO Crossing Fields
• Cowboy Bebop Tank
• Gurren Lagann Sorairo Days

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.

https://m.youtube.com/watch?v=vIhQ9zya2-g

Gundam the witch from mercury

Any jojo op but especially great days

https://m.youtube.com/watch?v=mU3vgXUKeFM

And this one

https://m.youtube.com/watch?v=BaoWJnC3V_o

PUT YOUR GRASSES ON

Welcome to the N.H.K. ("Puzzle" by ROUND TABLE feat. Nino) is one of my favourite openings

Harukaze by Scandal

My favorite opening is probably Akame Ga Kill. Either that, or Angel Beats

1. Inner Universe from GitS: SAC - if cyberpunk had a theme song, it would be this.

2. No Separation from Heaven Official's Blessing - a warm, slowly building love song with a hint of loss and longing.

3. A Cruel Angel's Thesis from NGE - an energetic, action-y song with darker undertones.

Ok I got more

Komi can’t communicate

https://m.youtube.com/watch?v=xHlx3rx5Bew

Gundam iron blooded orphans

https://m.youtube.com/watch?v=82HM0z6qd20

Black lagoon

https://m.youtube.com/watch?v=dWfxcRj39tg

I'd have to pick Butter-fly from Digimon Adventure.

The one that's always stuck with me is Blood+ third opening to the song of Colors of the Heart by UVERworld.

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

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.

ClariS - Irony - OreImo season 1 OP

It's so gahdamn catchy

Death Note opening 1

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.

Maria+Holic Alive OP 1 Mousou Senshi Miyamae Kanako by Sugita Tomokazu

Land of the Lustrous' opening, Kyoumen no Nami, is my #1 most listened to song on Youtube Music two years in a row, so probably that.

Aside from that, some top picks are (in order of best to not as best)

Vivy: Fluorite Eyes Song

Gurren Lagann

Samurai Flamenco

Baccano

Akudama Drive (mainly for the visuals)

Sk8 the Infinity

Noir (also mainly for the visuals)

Last Exile

Nagi no Asukara OP2

Ao Ashi OP2

lotgh op 2

"In every age

In every place

The deeds of men

Remain the same"