Early on:
The Beatles
The Who
Deep Purple
Simon and Garfunkel
The Band
Cat Stevens
Elton John (the early albums)
Somehow out of this I started playing the blues . . .

And then:
Yes
Led Zeppelin
Genesis
Keith Jarret
Gentle Giant
Jethro Tull
Chick Corea
John McLaughlin
King Crimson
Emerson, Lake, and Palmer

And then I fell in with a folkie crowd, and was introduced to:
Steeleye Span
Martin Carthy
Lo Jai
Malicorne
Maluzerne
The John Renbourn Group
Pentangle
Melusine
Muzsikas
Sebo Consort
Kornog
The Silver Strings Macedonian Band
Alan Stivell
William Pint (a good friend and musical co-conspirator who has had a big influence on my playing).
Anna Peekstok (my wife, who consented to play music with me after finding that we both saw lots of similarities between Jethro Tull, Led Zeppelin, medieval music, European traditional folk, and the blues. She continues to amaze and influence me musically).

And a bunch of early music, most notably:
Thomas Binkley & the Studio der Fruhen Musik
Atrium Musicae de Madrid
Les Menestriers

Lately, a lot of Scandivavian, Flemish, and Dutch music:
Garmarna (especially the early albums)
Lais
Kadril
Frifot
Vasen

And, as someone said earlier, the songs themselves. I spend many happy hours pouring through books of old folk songs, finding the threads of different versions, the odd turns of phrase, the intensely satisfying melodies. This isn't done in any scholarly or folkloric way, although I suppose some of that sticks to me. It is just for the joy of the music.

John Peekstok