Mine is Transformers Generation 1 and my most favorite anime ever. i will always keep the toys.
Urashima Tarou
Idk if that counts, if it doesn't:
Dragon Ball Z
Alps no Shoujo Heidi
I received the DVD set as a gift from one of my dad's friends when I was very young and I binged it multiple times.
Unfortunately, I don't remember most of the plot apart from some very specific scenes and moments.
Also, more recently I found out that Hayao Miyazaki worked on it, if that interests you.
Dororo
Hoge hoge tara tara hoge tara pon
anilist.co/anime/3009
When I was kid in the 90s. It aired together with Jungle book and Captain Tsubasa, but it was my favourite, because I liked fighting shows.
The thread "What's the oldest anime you've completed?" and it's comments have been merged into this thread.
You can view the merged thread's body below:
I'm pretty sure this is mine.
Andersen Douwa Ningyo Hime
https://anilist.co/forum/thread/42320
This was done before
Edit: I was wrong
This is the oldest one I've completed, would definitely recommend it, it did lack a little character development but hey, it was 1907, still impressive!
Katsudou Shashin