Since my teenage years, I've been listening almost exclusively to Metal at home (of course I hear other kinds of music on radio).
When I want a change from Metal or something softer, I usually listen to Blink 182 or Boxcar Racer.
Starting to like Angels & Airwaves.

Some U2, Journey, Styx, etc can also do.
Unlike lots of Metalheads though, I hate hard rock in general.

Tons of bands...
I love The Byrds and The Stones...
That said, i will keep it in the music i listened to the most when i was a teenager back in the 80's (non-metal bands from the 80's):
Sonic Youth, Pixies, REM, Dinosaur Jr, The Jesus and Mary Chain, Joy Division, The Cure, The Cult, The Church, Galaxie 500, The Stone Roses, The Sisters Of Mercy, The Long Ryders, Dream Sindicate, Violent Femmes etc
At that time i didn't, but i must say that now i think New Order were also great.

I second Sonic Youth, they are the shit. I like Wilco, Radiohead, REM, and even the most recent Opeth because that is not metal, but i like it. Some killer Allman Brothers type guitar duels in that, and I dig the guitar duel kinda thing.

Given I like guitar in general; Frank Zappa when he's not talking about finger-banging his sister, Junior Brown is a pretty awesome country slide player, Doc Watson is awesome as well.

Plus Classical and Jazz. I either absolutely love both genres or find them utterly shit. There is no in-between on Classical or Jazz stuff. It either sucks or I want everyone in a three-mile radius to shut the fuck up so I can enjoy it!!!

I don't really consider myself a massive metalhead (though the mirror would disagree with "not massive" ), so I listen to quite many non-metal bands. I love Radiohead for example. I think Thom Yorke and Johnny Greenwood are right up there with the greatest songwriters of all time and somehow - with the exception of "Pablo Honey", Radiohead have never released a bad or mediocre album. I think after "Creep" became a hit and after "OK Computer" won them all the accolades, they could have sold out and cashed in so big, but they went in the opposite direction and forever solidified their status as an all-time great band with Kid A.

My two favorite genres in addition to metal are prog and punk rock. I almost never listen to either genre on the same day or week, however. Both genres sort of come and go. Some weeks I will listen to nothing but Pink Floyd, King Crimson, Rush, Spock's Beard etc and another week I will only listen to The Sex Pistols, The Clash and some punk bands from my native country, such as Vennaskond, J.M.K.E. and Singer Vinger.

And also, I absolutely love David Bowie.

Nhors non metal albums are amazing!