Not sure what the situation on METAL is here, but I'll go ahead...
Northlane - Quantum Flux. One of the best songs I've ever heard really. It's a mix of soft rock, and Metalcore. Not like anything overbearing like you typically get with Metalcore, and it has an incredibly catchy hook.
http://m.youtube.com/watch?v=MIajmLP46b4
Now here we have Tool - Parabol/Parabola. Maynard (the lead singer) has a mesmerizing voice, and can go from soft to heavy in a heartbeat. Not like Death Metal growls.
Anyway this song is pretty long... Around 9 minutes I think. But the song is actually 2 different songs. Parabol prequels Parabola. Parabol is a slow melody thing, and then Parabola is fast Hard Rock thingamajig. I HIGHLY recommend you listen to their other songs, like Reflection, Vicarious, Jambi, H., Aenema, Sober, Third Eye, Stinkfist, Hush and so forth. It ranges from really heavy, to progressive ambient metal, to hard rock, and alternative rock.
http://m.youtube.com/watch?v=tvqOTjq0AjE
Now here we have Gojira - From Mars/To Sirius. Same two part song thing going on. From Mars is a slow melodic ambient thingy, and To Sirius is a heavy Death Metal song. It's really high quality, and it has a catchy riff/hook. I recommend you look up some of their other songs like, Oroborus, Flying Whales, L'enfant Sauvage, Vacuity, A Sight To Behold, Explosia, and Ocean Planet.
http://m.youtube.com/watch?v=d5fs5ELeJ1Q
And here is Deftones - Leathers. Leathers is a very heavy metal/nu metal song. Unlike most songs I've heard before, It conveys emotion extremely well. Catchy Hook. Check out their other stuff, Diamond Eyes, You've Seen The Butcher, Rosemary, Tempest, Change (In The House of Flies) and so forth.
http://m.youtube.com/watch?v=sPO81Fz4s2g
And that is all for right now