In no particular order:
*Everything must go - Chemical Brothers (GT1 US intro)
*My favorite game - The Cardigans (GT2 US intro)
*Plush - Stone temple pilots (GT2)
*Paranoid - Garbage (GT2)
*Are you gonna go my way remix (GT3 US intro)
*Turbo Lover - Judas Priest (GT3)
*Free wheel burnin' - Judas Priest (GT3)
*Hero - Foo Fighters (GT3 ending 1)
*Panama -Van Halen (GT4 US intro)
*Not Listening - Papa Roach (GT4)
*Getting away (with murder) - Papa Roach (GT4)
*Summer song - Joe Satriani (GT4)
*Moon over the castle - Long GT4 ending version
*Automatic remix - Weezer (GT5 Prologue intro US version)
*Survi3 - Daiki Kasho (GT5 Prologue intro EU version)
*Moon over the castle - GT5 Prologue ending version (best version)
*5oul on d!splay - Daiki Kasho (GT5 Spec II intro)
*Words - Goose (GT5)
*Patterns - Band of Skulls (GT5)
*Looking for you - Daiki Kasho (GT6 intro)
*Aliv3 - Daiki Kasho (GT6)
*We are one - Daiki Kasho (GT6 ending)
*Edge of the world - Daiki Kasho (GT6)
*It's all about you - Daiki Kasho (GT6?)
*Place in this world - Daiki Kasho (GT6)
*Lazy bones - Wooden Shjips (GT6) Let me note that I hated both songs of this band, but I'm kind of liking them no. Not as a GT soundtrack, but the songs themselves.
*Looking out - Wooden Shjips (GT6) My most hated song, but that now I like a lot.
*Sweeden - Amon Tobin (GT6) <== Kick butt song. I had a similar one in my Personal BGM in GT5 called Fools Rhythm. I was surprised they added this artist to the official list in GT6, and with a song that is virtually identical.
And there you go. I might be missing a few, but it's been so long since I have played any GT older than 5 that I only remember the ones that I really liked.
I am a rocker by heart, love everything from Trash, Heavy Metal, Black, Death, Symphonic, Progressive, but I'm not close-minded like the typical long haired metal heads. I'm tolerant towards liking other music too, like classic, Electronic, Nu Metal, Alternative, Fusion and experimental stuff. GT has obliged to my tastes.
I must say without fear of being wrong that GT6 has BY FAR the best OST in all the series. I haven't even touched the Personal BGM option and I doubt I will. Daiki Kasho in particular has really earned my admiration in GT6; he's a really kick ass composer and hope to hear more of him in future titles.