I guess you could say I listen to a lot of "non metal" because I listen to other stuff much more than metal.
prog rock (Rush, Yes, VDGG, etc), post rock (God Is an Astronaut, Red Sparowes, etc) punk rock (Everything from AFI, Misfits, The Descendants, to City Lights, early Blink 182, Offspring, The Story So Far, etc), hardcore (everything from Terror and Stuck Mojo to Ignite and Stick To Your Guns, to From Ashes Rise, Refused, Comeback Kid to The Acacia Strain, A Day To Remember, The Ghost Inside, to Spazz, Despise You, Magrudergrind, to Jawbreaker and Rites Of Spring etc), hip hop (Aesop Rock, Wu Tang Clan, Death Grips, POS, etc), new wave (Depeche Mode, The Smiths, Joy Division, etc), shoegaze (My Bloody Valentine, Slowdive, Hum, etc), classic rock (Boston, The Moody Blues, Pink Floyd), folk rock and neofolk (Comus, Fleet Foxes, Rome, Death In June Seelenlicht), top 40 pop (Lady Gaga, Ke$ha, Rihanna, Michael Jackson etc) singer/songwriter (Regina Spektor, Bob Dylan, Tom Waits, Frank Zappa, etc), industrial (Nine Inch Nails Kraftwerk, Light Asylum, etc), drone (Earth, Sunn O))), etc), indie rock (Frankie Rose, The Pains of Being Pure at Heart, Vampire Weekend, The Drums, A Place to Bury Strangers), assorted electronic (Tiesto, Kavinsky, LMFAO, Justice, Pendulum, Chromeo, Zedd, etc) dubstep (Skrillex, Borgore, Nero, Dubba Johnny, Reso, etc), some jazz/fusion (Allan Holdsworth), and assorted "modern rock" (Dredg, Oceansize, Foo Fighters, Deftones, Alice In Chains, Mew, Coheed and Cambria, Muse, Minus The Bear, etc)