This song is a classic, I can't even find a video that has the ED and the song together:
Koibito ga uchujin nara (If My Lover Was An Alien) by Junko Iwao
This is a more recent one that's really grown on me even though the anime just ended a week ago:
Oren-ji by Rie Kugimiya, Yui Horie, and Kitamura Eri
And this one is a personal favourite that is also my ringtone:
Akane-iro Hometown