Wow, some great selections. My all time favourites are bands like Cold Chisel, Talking Heads, Queen, and Bruce Springsteen. However, I do enjoy a fairly wide range of music.
Australian bands like Cold Chisel, AC/DC, Midnight Oil, The Black Sorrows, Hoodoo Gurus, Mental As Anything, The Angels, Paul Kelly, and Crowded House (well OK, really a Kiwi band).
60s and 70s stuff like The Doors, Rolling Stones, The Animals, Beach Boys, The Beatles, Bob Dylan, Creedence, Eric Clapton, John Fogerty, Zeppelin, Pink Floyd, Santana, Steve Miller Band, and Van Morrison.
80s music from Bruce Springsteen, Talking Heads, John Mellencamp, Dire Straits, Billy Joel, Elton John, Lloyd Cole and the Commotions, Eurythmics, The Police, and David Bowie.
Jazz is great when I am in the right mood, particularly the incomparable Miles Davis, John Coltrane and Nina Simone. More recent fun jazz is The Lost Fingers.
I have always enjoyed Blues with a bit of edge, particularly George Thorogood and the Destroyers, John Lee Hooker and Ry Cooder.
I have occasionally been found stomping my feet to country music after watching "Walk the Line", so Johnny Cash and the Dixie Chicks.
I am not too familiar with classical, but my wife listens to it all the time and I actually quite enjoy it. I like listening to good guitar work, especially John Williams, so Flyor64's recommendation of Rodrigo y Gabriela was excellent. I also put Mark Knopfler in this category.
And finally, I am more and more enjoying "alternative" and occasionally quieter rock music like Arkells, Beck, Ben Harper, some of Ben Lee's stuff (Awake is the New Sleep), City and Colour, The Corrs, Cowboy Junkies, Elliott Brood, Franz Ferdinand, The Fray, Jack Johnson, Jason Mraz, The Killers, Neko Case, Dido, Norah Jones, Nickelback, Sarah McLachlan, Serena Ryder, Stone Temple Pilots, and Alanis Morrisette when she is angry!