[Utena]

moumoon - Blue Rain http://nhacso.net/nghe-nhac/blue-rain.WlxYV0dc.html
MiChi - RAiN
Mika Nakashima - Helpless Rain http://www.jpopsuki.tv/video/Mika-Na...dfd0144d83d97a
Ai Otsuka - Ame no Naka no Melody https://www.youtube.com/watch?v=s3QKOROdwBM
Hitomi Shimatani - Rainy blue https://www.youtube.com/watch?v=ZZJcL23IlbY
Kou Shibasaki - Saiai https://www.youtube.com/watch?v=34KmSC_-xgg
Masaki Yuka - Summer Rain https://www.youtube.com/watch?v=J_q6Y1U5gVM
Kana Nishino - if https://www.youtube.com/watch?v=egXVuWWLr4o
BENI - Satsuki Ame https://www.youtube.com/watch?v=7E7BoRjo7hs
BENI - a million jewel https://www.youtube.com/watch?v=NQiNjaGmnBg
Crystal Kay - Sugar Rain https://www.youtube.com/watch?v=Xq4H9eI3im8
GIRL NEXT DOOR - Fine after rain
JAMOSA - RAIN
jyA-Me - 涙 rain
Miz - In The Rain
OLIVIA - Rain https://www.youtube.com/watch?v=9Vx-4CO4EIg
Angela Aki - Rain https://www.youtube.com/watch?v=yhBBa6SgrK8

Some others that have no direct link with rain but make me think of rainy days somehow

Aya Kamiki - Summer Memories https://www.youtube.com/watch?v=yVNMgVQ_XZE
Mika Nakashima - Kumo no ito https://www.youtube.com/watch?v=oCMBogdhmMM
Yuna Ito - Faith http://www.jpopsuki.tv/video/Yuna-It...4da2be71ec0c34
Ai Otsuka - Kingyo Hanabi https://www.youtube.com/watch?v=s7pbJf_Rybc
Maki Goto - Tears drops https://www.youtube.com/watch?v=-F5WrqvmmQI
Yui Aragaki - piece https://www.youtube.com/watch?v=z198GrbbofU
CHiE - Kagi Wo Kakete https://www.youtube.com/watch?v=GuzqL81tjg0
JYONGRI - Free my soul
YU-A - Soba ni ite, sugu kiete. https://www.youtube.com/watch?v=YsLwfRmg-4k
Miliyah Kato - Summer Time Lonely http://val.fm/summer-time-lonely-miliyah-kato-mp3/
Satomi Takasugi - Hyaku Renka https://www.youtube.com/watch?v=eNWmY4-bUUY