This is not the discussion about which song is best. Rather it is about songs that left a mark on Animated Film music history, for good or ill. Some songs that isn't good may need to be mentioned for its positive or negative effects. However, music is about impression; if people didn't like it, it will be forgotten. Do feel free to discuss your feeling for the song, for how you felt about the song was likely part of the reason why some song writers remember it and use it.
I am going to run a class of importance rank in this thread. Feel free to do what you like as well.
Here is some of my songs.
1970s: Mazinger Z's theme song - S class. For most Koreans, it is the epitome of the anime songs. Enough Japanese remember this song to follow along if a Korean sings it near by. If Tens of millions of people still can sing this song even after 30 years, you just cannot ignore its impact.
1983: Ai, Oboete imasuka? ( Macross the Movie ) - SSS level. This is the song formally launched anime music industry. To tell the truth, an apt comparison to Western European Music History might be Josquin Dez Prez.
http://en.wikipedia.org/wiki/Josquin_de_Pr%C3%A8s
1990s : Tori no Uta ( AIR ) - SS level. One of the most well composed and performed song in the history. This is the song that hailed the rise of Key, Kyoto Animation, and Eroge anime adaptation. Not only that, this is a song that is immensely popular to people who never watches Anime. I remember Lia filling up large concert halls in Korea as recently as 3 years ago, and it was a personal concert, not an Anime concert, so most of songs were of no relation to Anime, thus most of the audience were fans of Lia, not Anime watchers. Yet, the song that received most enthusiastic welcome still was Tori no Uta. If there is one song that should be used in text books for popular music composing students, this is it. In fact, I believe it already is used as such.
2000s : Hare Hare Yukai - SSS level. Music theory speaking, this is not something profoundly new nor innovative. It was the dance, but its world wide impact may have been the greatest in Anime history. You just can't ignore this.
2000s: Lucky Star Opening - S+ level . First thing that I said after seeing this was 'Kyoani sure knows marketing.' This song raised fast performance and rapidly changing videos to a new level.
More to come later.