From this list here. This was the best I could find when looking for a list of "classic" Japanese songs. English sources that talk about J-pop mostly focus on idols or anime songs. The list is a bit outdated, but it covers a good variety of genres.
1. Southern All-Stars
tsunami (2000)
涙の海で抱かれたい ～sea Of Love～ (2003)
2. YMO (Yellow Magic Orchestra)
firecracker (1978)
solid state survivor (1979)
3. Yumi Matsutoya
ひこうき雲 (1973)
ルージュの伝言 (1975)
4. Happy End
風をあつめて (1971)
夏なんです (1971)
5. Hibari Misora
川の流れのように (1988) - voted best Japanese song of all time in 1997
愛燦燦 (1986)
6. Tatsuro Yamashita
Ride On Time (1980)
Christmas Eve (1983)
7. Momoe Yamaguchi
さよならの向こう側 (1980)
秋桜 (1977)
8. Yosui Inoue
夢の中へ (1989)
少年時代 (1990)
9. Eiichi Ohtaki (member of Happy End)
君は天然色 (1981)
さらばシベリア鉄道 (1980)
10. Seiko Matsuda
風は秋色 (1980)
あなたに逢いたくて ～Missing You～ (1996)
11. Ryuichi Sakamoto (member of YMO)
Merry Christmas Mr Lawrence (1983)
bibo no aozora (1996)
12. Keisuke Kuwata (member of Southern All-Stars)
明日晴れるかな (2007)
白い恋人達 (2001)
13. Motoharu Sano
Visitors (1984)
アンジェリーナ (1980)
14. Eikichi Yazawa
止まらないHA～HA (1986)
I LOVE YOU, OK (1975)
15. Flipper's Guitar
恋とマシンガン (1990) - highlight of this quarter of the list for me.
Groove Tube (1991)
16. RC Succession
I LIKE YOU (1990)
Transistor Radio (1980)
17. Kenji Sawada
時の過ぎゆくままに (1975)
勝手にしやがれ (1977)
18. Kyu Sakamoto
上を向いて歩こう (1961) - aka Sukiyaki. The only Japanese song to top the Billboard 100.
坂本九見上げてごらん夜の星を (1963)
19. The Blue Hearts
Linda Linda (1987) - heard it in Osu! Tatakae! Ouendan
Train-Train (1988)
20. Miyuki Nakajima
わかれうた (1977)
地上の星 (2000)
21. Tetsuya Komura
Running to Horizon (1989)
I want you back (1989)
22. Boowy
Marionette (1987)
わがままジュリエット (1986)
23. Yutaka Ozaki
I Love You (1991)
Oh My Little Girl (1991)
24. Hikaru Utada
First Love (1999)
travelling (2001)
25. Tamio Okuda
愛のために (1994)
息子 (1995)
Top 100 Japanese Pop Artists Pt. 1
