Critic Mark Deming wrote that "Quine's eclectic style embraced influences from jazz, rock, and blues players of all stripes, and his thoughtful technique and uncompromising approach led to rewarding collaborations with a number of visionary musicians.

"[1] His collaborators included Richard Hell & the Voidoids, Lou Reed (notably on The Blue Mask), Brian Eno,[2] John Zorn, Ikue Mori, Marc Ribot, Marianne Faithfull (Strange Weather), Lloyd Cole, Matthew Sweet and Tom Waits.

Lester Bangs wrote that he was a "pivotal figure" and "the first guitarist to take the breakthroughs of early Lou Reed and James Williamson and work through them to a new, individual vocabulary, driven into odd places by obsessive attention to On the Corner-era Miles Davis.

[9] Throughout his San Francisco years (coinciding with his attempts to pass the California bar exam), Quine "sort of began to come up with my own style," often performing under the influence of LSD; nevertheless, he disdained such psychedelic rock groups as Jefferson Airplane and the Grateful Dead.

[2] During this period, his influences included John Coltrane's Ascension (1966), Elvis Presley's singles for Sun Records, Fats Domino, Bo Diddley, James Burton, Mickey Baker and Little Richard.

[2] Upon moving to New York, he began to gravitate toward a new array of influences, including the 1972-1975 electric oeuvre of Miles Davis (especially the guitar sounds on 1972's On the Corner and 1975's Agharta),[10] The Stooges' Raw Power (1973) and Brian Eno.

[2] After leaving Prentice Hall to focus on his musical career in the mid-1970s, he worked at the Greenwich Village bookstore Cinemabilia with Richard Hell and Tom Verlaine, the co-founders of the influential punk band Television.

[16] Throughout the 1980s, Quine made appearances as a session player on records by Tom Waits, John Zorn, Marianne Faithfull and Scritti Politti.