Mostly are from the 80s. I only included the animes I have watched from these years. I'm not including Sequels from anime that started on previous years. I am including Sequels where it makes sense to keep watching, in order to complete the story.
From both in local TV and cable TV:
A Little Princess Sara
A Little Snow Fairy Sugar
Ah! My Goddess
Ai to Yuuki no Pig Girl Tonde Buurin (Super Pig)
Akazukin Chacha (Red Riding Hood Chacha)
The main similarity of each anime in this list is always a girl (or fragile person), who seeks protection or is protected by a second party. Mostly romantic feelings included.
(Also, since this covers my favourite "genre", basically my top fav...