Joshiraku is about five rakugo-performing girls. The first episode opens with the end of a performance by one of them (to an audience of mostly empty seats), then the OP. Okay - at this point, I don't really know what to expect, other than likely low-key humor.

Then it moves to them in a dressing room in which most of the series takes place, kneeling around a table. The camera focuses on one of them, then after an awkwardly long silence, she says, "You should just read the manga instead."

I was sold right then and there.

Monogatari Series.

This is the first 45 seconds of the first episode:

It's really perverted but I've never seen perversion presented in such a way. I instantly knew it had a different kind of "language" in anime. I love every second of it. ^and^ ^i^ ^love^ ^hitagi^ ^so^ ^much^

I am going to exclude any shows for which I had previously read a manga or novel version of the story. There are a couple shows I can think of where I knew after episode 1 that I was in for a good time:

• Kino's Journey (2017) - The first episode is excellent and really sets the tone for the kind of show you are in for. It's really, really good.
• Heavenly Delusion - I went in completely blind to this show and was blown away. I was instantly hooked and after the show ended I binged the entire manga, keeping up with it to this day. The OP is excellent as well. Unfortunately no season 2 announcement though.
• Little Witch Academia - I love LWA and I fell in love with the world and characters right from the beginning.
• Konosuba - As somebody that has read/watched way too many isekai over the years, this show hit the humor sweet spot for me basically as soon as Aqua entered the picture.

There are two main categories of being special to me.

The first is when characters show some maturity - or just a lack of stupidity - in their thoughts and behaviour in the first episode. Some examples include:

• Thors from Vinland Saga
• multiple characters from Frieren
• now that I think about it, plenty of anime from my Peak Drama list fits this criterion

These anime would end up having stories, characters and writing that are top-notch, clearly a cut above the rest.

The other is when the show subverts expectation by not following stupid tropes from the start; these are usually parodies. Some examples include:

• Cautious Hero - dude who got isekai-ed isn't some loser to begin with (i.e. no wish-fulfillment)
• Konosuba - dude who got isekai-ed did not get cheats (i.e. no power fantasy)
• 100 Girlfriends - dude with a harem is not a wimp who can't handle girls (i.e. no self-insert for losers)

These anime are special by virtue of being different from peers of the same genres / subgenres.

The beginning of Redline gave me the impression that the whole movie would just be a sequence of cool shit happening, and then the whole movie was a sequence of cool shit happening. It ended up being one of my all-time favorites, and proved to me that an anime doesn't need a complex story to be excellent.

Frieren

I usually pick out my anime carefully. I don't watch that much so I don't want to pick something that is ass. I also tend to finish everything I watch. So usually I pick out things that I quite like.

In the beginning of liking slice of life I didn't know what to expect and if I liked it so I didn't guess before watching that I would be into it. However it changed with Lucky Star. I watched a few clips on youtube and thought, man this is going to be great. And it was! While watching the very first scene where they eat lunch I just thought "this is the shit". Lucky Star really confirmed to me that SOL was my thing.

hyouka and haruhi maybe

• oh also lain

Some of the shows I found had great opening scenes and became favourites:

• Shadows House
• Ancient Magus’ Bride
• Medalist
• Ascendance of a Bookworm

Late response, but I thought about this question for a (long) while...

And I eventually settled on Suzumiya Haruhi.
Whilst not really one of my favourite anime any longer, it really appealed to a teenager profoundly bored with modernity.

Edit: Oh and Toradora! perhaps, I should really rewatch that.

Outlaw star.

Golden time

Shigatsu wa Kimi no Uso