The actual list of bands and artists that I like would be much too extensive to list fully, to be honest. I like just about every kind of music there is out there, to some extent.
As for bands or musicians that have had a direct influence on what we play, speaking for myself, I find alot of influence and inspiration coming from stuff like Pink Floyd, Led Zeppelin (especially albums like "Led Zeppelin III", I feel they always shined when focusing on more acoustic material), Pyogenesis (albums like "Twinaleblood" really showed me that you could meld doom-death metal heaviness with pop and straightforward rock sensibilities and melodies), Amorphis (especially Tuonela and Am Universum), Black Sabbath, Candlemass, Trouble, Winter, Celtic Frost (Into the Pandemonium especially....in fact, if you listen to a song like "Last God", that song is basically Celtic Frost and Winter meshed together, with the ND touch added!), Voivod, Entombed, and even local bands that I grew up with like Contagion and Maimed had a great affect on my playing and the style I developed.
As for the stuff I just like and enjoy in general, I really like: KISS, Cheap Trick, Carcass, H.I.M, The 69 Eyes, Morbid Angel, Opeth, Katatonia, Alice Cooper, David Bowie, T. Rex, Captain Beyond, Norah Jones, Fleetwood Mac, Roy Orbison, Radiohead, Coldplay, Death, The Doors, Gorefest, Atrocity, Secret Discovery, In Flames, Darkseed, Yes, Van Der Graaf Generator, Motorhead, Backyard Babies, Hanoi Rocks, Motley Crue, Ratt, Megadeth, Anathema (Alternative 4 and newer), Iron Maiden, Judas Priest, Journey, King Crimson, Mercyful Fate/King Diamond, Raven, Exciter, Possessed, Sodom, Mekong Delta, Holy Terror, Fastway, W.A.S.P (first album particularly), A Perfect Circle, Shadows Fall, Soil, Sindrome, USURPER (new album is fucking great), Pantera, Damage Plan, Wickerman, Sleep, Crowbar, America, Guess Who, Mary My Hope, Acid Bath, Agents Of Oblivion (incredible!!), Edge Of Sanity, Sentenced, Journey, Boston, Duran Duran, Abba, Adam Ant, Disharmonic Orchestra, Watchtower...........man this could go on forever, but I really do love all of the aforementioned artists, and there's many more.
I think you're going to find that the other guys in the band also have a pretty eclectic mix of tastes as well, which explains alot about us, I believe!