I'm not quite sure, if that counts for all anime or only anime when I already knew what anime actually was. Anyway, I'll just take both.
My very first anime from my childhood:
Heidi, Girl of the Alps is based on the novel by Johanna Spyri and became the very first series of what would later become the World Masterpiece Theather (WMT for short). It's about a little girl called Heidi, who goes to live in the Alps with her grandfather and later goes to Frankfurt to become the play mate of a sick girl called Klara. This show is a cult classic in Germany, pretty much every one I know saw this one as a child in some form.
Here you can see the German opening and ending for the show:
Now onto the first anime I saw after I actually learned what anime is.
Yup, another cult classic. I don't think I need to summerize what this movie is about, do I? But I will say that I do like the manga better, but I totally get why they changed things for the movie. To adapt the whole manga, it would need a tv series or at least an OVA. So I'll leave you with a rousing rendition of "Tetsuoooo!" "Kanedaaaaa!".
Day 1 - Very first anime Day 2 - Favorite anime you’ve watched so far Day 3 - Your anime crush Day 4 - Anime you’re ashamed you enjoyed Day 5 - Anime character you feel you are most like (or wish you were) Day 6 - Most annoying anime character Day 7 - Favorite anime couple Day 8 - Most epic scene ever Day 9 - Saddest anime scene Day 10 - Favorite slice of life anime Day 11 - Favorite mech series Day 12 - An ecchi picture from your favorite series Day 13 - Cosplay of your ‘waifu’ or husbando’ Day 14 - Current (or most recent) anime wallpaper Day 15 - Post a cute Neko-girl Day 16 - Post a kigurumi cosplay of your favorite anime character Day 17 - Favorite tsundere Day 18 - Something moe Day 19 - Mandatory swimsuit post Day 20 - Favorite shoujo anime Day 21 - Best yandere character Day 22 - Favorite boy’s love couple (or yuri couple, if you don’t like that sort of thing) Day 23 - Anime you think had the best, or most intriguing art Day 24 - Favorite anime hero or heroine Day 25 - Best anime villain Day 26 - Your favorite harem anime Day 27 - Favorite anime opening theme song Day 28 - Favorite pokemon Day 29 - Favorite school uniform Day 30 - Favorite anime ending theme