Here is a nearly complete listing of Puffy's recorded songs. The letters signify what info is still needed: C = Credits, R = Romanji, E = English.

Ai no Aura (Auro of Love)- E
Ai no Shirushi - C
Ai no Shirushi (Chinese version)
Ain't Gonna Cut It - E
Aishuu de Ito {New York City Nights} - R E
Always Dreamin' About You
Angel Of Love - R
Angel Wink - R
Asia no Junshin (True Asia)
Basket Case
Be Someone Tonight
Beginnings (Hajimari no uta - The Song of Origin)
Blue Tears (Aoi Namida) - E
Boogie-Woogie No.5
Boom Boom Beat
Brand New Days (Atarashii Hibi)
Cake is Love - C
Call Me What You Like
Cameland
Can-nana Fever - R
Cherry - E
Choushou (Ridicule) - E
Closet Full of Love - R E
Complaint - R E
Cosmic Wonder - E
Dare ga Sore o - E
De Rio - C E
December
Destruction Pancake - R E
Don't Bring Me Down
Electric Beach Fever
Etude
Forever
Friends - R
Friends Forever
Girls Just Want to Have Fun
Go Baby Power Now
Green Apple - E
Hanabi - E
Harada Kinenbi (2000 Hit-n-Run All Stars) - C R E
Haru no Asa - C E
Hasan Jauze - R E
Hataraku Otoko - E
Hataraku yo - E
Hayai Kuruma - R E
Hazumu Rhythm - R E
High Teen Boogie - R E
Hi Hi
Hito ni Yasashiku - R E
Hito Natsu no Keiken - C R E
Honey - E
Hurricane (Harkiken) - C E
Island - R E
Image Down - R E
Into the Beach (Umi e to)
Invisible Tomorrow - R E
Jet Keisatsu
Joining a Fan Club
K2G
Kakkoman Boogie (Parenthesis Man Boogie) - R E
Kazemakase Futaritabi - R E
Kimi ga Suki - R E
Kimi to Ootobai - R E
Kireina Namida ga Tarinai yo - E
Koino Line Aino Shape
Kokoro ni Hana wo - Flowers to the Heart - R E
Kore ga Watashino Ikiru Michi - E
Korega Watashino Ikirumichi (Chinese version)
Kuchibiru Motion - R
Lemon Kid - E
Long Beach Nightmare - E
Love Depth - E
Love so Pure
Lucy In the Sky With Diamonds
Lucy wa Moon Face - R E
Missing You Baby

Mole
Mole-Like
Mother
Nagaiki Shite ne - E
Nannari to Naru Deshou - E
Natsuyasumi Prototype - R E
Nehorina Hahorina - C
Neji Potion - R E
Nice Buddy
Nichiyoubi no Musume (Sunday girls)
Oh Edo Nagareboshi IV - R E
Onna Machin Gan
Onnanoko Otokonoko (Boys and Girls) - E
Oriental Diamond - R E
Otomemoriaru - E
Peace - R E
Planet Tokyo
Puffy de Bossa
Puffy de Rumba
Puffy na Ohirune - R E
Puffy no Hey! Mountain - E
Puffy no Tsuaamen - R E
Puffy's Rule - R
Radio Tokyo
Red Swing - E
Robot Proto-type Version 0.2 - R E
Sakura Saku - E
Sayonara - R
Sayonara Summer - R E
Security Blanket
Sekai no Hajikko - R E
Shall We Dance
Shiawase (Happiness) - R E
Shoubijin - C R E
Shut Your Mouth, Honey (Mondou Muyou) - R
Sign of Love - C
Simple - E
Snacks - E
So Long Zero
Sorenarini (Hold Out As Long As You Can) - E
The Story
Stray Cats Fever
Su-i-Su-i - R E
Sui Sui - R E
Sumire (Violet)
Sunday In The Park
Sunrise
Swimming Pool - R E
Tadaima (I'm Home) - E
Taiyou - E
Tararan
Teen Titans Theme
Teen Titans (Japanese version)
Tennen no Beauty (Natural Beauty) - E
Tetsugaku - C E
Thank You
That's Sweet Smile - E
That's The Way It Is
This Is the Song of Sweet Sweet Season... - R E
Tokusuru Karada - E
Tokyo I'm On My Way
Tokyo Nights
True Asia (Asia no Junshin)
True Asia (English version)
Tsuyoki na Furari - E
Turn It Into Love (Ai ga Tomaranai) - R E
Umi no sei - E
Urei - R E
Usagi Channel
V-A-C-A-T-I-O-N
Watashi no Nozomi (My Wish)
Wild Girls on Circuit (Circuit no Musume)
Youkai Puffy - R E
Your Love Is A Drug
Yuki ga Furu Machi - R E
Yume no Tameni - E

The Song Finder Videos are a great way to track down the name of a Puffy song you've heard. Check it out.