Chronology-wise the first episode of Berserk takes place after the last episode considering Guts already has his prosthetic arm and missing eye. Even though this is how it works in the manga, with his time with the Band of the Hawks being a flashback, the episode doesn’t follow the manga and I’m still unsure if it follows the overall plot at all, as you are never really sure if the Count at the start was Griffith or not. I personally think the films did it right by starting chronologically at the beginning, introducing the character when he was younger and building him up towards the terrifying climax.
Once again we have a first episode that takes place in the future but this one is set halfway through the anime and without giving any context as to what’s going on what’s actually going in the first episode. It’s very strange and slow paced with action that more or less confuses you than makes you want to watch more. Like Berserk the second episode is where the story begins and despite the creators intentions to intrigue you with the cool character Brandon Heat was to become, it just made me feel like it was going to be another bad post apocalypse anime until I finally got around to watching episode 2 and really got into it.
The Melancholy of Haruhi Suzumiya
If you’re going by the chronology that it was aired in, the first episode of The Melancholy of Haruhi Suzumiya, or episode ‘zero’, was not really the first episode but a short film they make during the second season. Watching this episode first could give the impression that the entire anime is going to be about a bunch of high school students making amateur movies and for an anime that doesn’t really get interesting until the end of episode 3 you really don’t want to suffer through this unnecessary prologue.
Neon Genesis Evangelion
Now this one is more my opinion than general consensus but I personally think you should the skip the first episode of Eva. Watching it this way not only do you skip Shinji’s squealing from episode 1 but you get dropped right into the tense scene when he’s about the fight Sachael without any need to go through the 10 minute preamble of jargon and badly scripted emotional baggage. It’s almost like Anno learnt to write in-between episodes 1 and 2 because the amount of telling instead of showing that goes on in the first episode in comparison to the second is insane.