Flag - "Hope to Peace" by Ike Yoshihiro
https://www.youtube.com/watch?v=4Wfv6FjzHbw

We’ve got some dull people in this thread. Some of you fail to provide video links and most of you don’t even bother to add a line explaining your picks.
Come on, peeps; share a little.

Revolutionary Girl Utena’s Rondo-Revolution. I’m deeply ashamed for forgetting to add this in my first post.
Besides having some cool visuals, it also has that mystery factor going for it. If you’re not wondering what’s the deal with that upside-down castle, you’re wondering why there’s two girls revolving at the start but only one at the end. What happened to her? I must watch to find out…
I enjoy that trope where fragments of earth crumble and rise upwards, this opening has a gorgeous example of it at 1:05. And what’s up with those flying horses? They don’t even have wings. This opening spits in the face of physics.

The Duke of Death and his Maid’s Full Moon and Silhouette's Night. An adorable duet. It’s a small touch- but I love that lip-sync on Alice near the end.
There’s a nice gag hidden behind Cuff’s fire magic burning the character at the end of the wheel; poor Walter sees himself as the forgotten second son of his family, so of course the opening mistreats him like a last minute addition, not even granting a clean portrait to introduce him.

Death Note’s What's Up, People?!. Has any 2nd opening ever shocked its viewers like this one did? And who doesn’t enjoy a good Slipknot-style scream?
This also happens to be the source of one of my favourite AMV Hell skits.

Too many to count. Like Chaz, I'll just post 3 and go into it a bit.

Ghost in the Shell: Stand Alone Complex's Opening. Feels like this time capsule of the hopes and ambitions the industry had about the ease of CGI. So each and every decisions on the artistic front is there to make and feel like it's something mechanical of another being, yet still human. That, and it was inspired by Kanno's song hitting the same themes about spirits, knowledge of what's out there, and so on. Just an incredible way to get in the head space of what's to come.

Ojamajo Doremi Dokkan's OP. Perfect summary of what makes Doremi's comedic moments something special: impeccable timing, vivid color theories, and themes of love, community, and individualism expressed in a matter that can only happen under the experience of Toei.

Clannad: After Story's OP. (forgive the 60 FPS thing) A masterclass of visual storytelling: warns you for the emotions that's about to come, but is told in a way that makes you remember it with a faint smile than outright depression.