Ok, I have over 5,000 various songs saved to my phone, so I know a little about good music. Here are some of my favorites:
(Band followed by a couple songs)

Matchbox Twenty
Real World
Push

Chevelle
Hats Off to the Bull
Family System
The Red

Poison
Unskinny Bop

INXS
Devil Inside
Suicide Blonde

The Offspring
You're Gonna Go Far, Kid
Why Don't You Get A Job?


 Hope you enjoy these songs! If not, then I am sorry. But I am sure you'll like 'em!

the number one: hey about checking out these artist:wild child by ENYA,  already gone by Kelly Clarkson, set the world on fire by BRITT NICOLE, and finally come to the rain by Taylor swift.                                                                                                                                                                                                                                                                         

I have a suggestion!
Frére Jacques...
https://www.youtube.com/watch?v=BC6rvbxdywg


That's all I can suggest, honestly
So I'll just do a random song

And then I figured a song had a lyrics
https://www.youtube.com/watch?v=cd7OHbulNXU
loooool Sorry for the childish songs, btw, I just like the first one

Some good anime songs that you might like to listen too. 

Shakugan no shana Ed 1
http://www.youtube.com/watch?v=706WX21dCBY

No Game, No Life op cover Amalee
http://www.youtube.com/watch?v=stlbq_w3zrY

I know of a few songs that you might be interested in. 

Good with Grenades:
Bruises and Bitemarks

Disturbed:
Hell
Down With the Sickness
Indestructible

RWBY: (not a band or artist, but a show made by Rooster Teeth. I don't know the artist of the songs)
This Will Be the Day
Time to Say Goodbye

Lindsey Stirling: (mainly instrumental songs)
Shatter Me 
Master of Tides
Roundtable Rival

Anything from Halestorm


Alestorm: 
Wenches and Meade
Keelhauled
Wolves of the Sea
You Are A Pirate

I hope at least some of these pique your interest.

Song: Simple Man by Lynyrd Skynyrd. Another good song by Skynyrd is Traveling Man, as well as the infamous song by Skynyrd Mr. Saturday Night Special depending if your a gun lover or not you may hate that song, or play it as a ruse for the duality of man.

thenumberone : These aren't really songs as there is no singing in them, but still, it is very good music.
The band is called Two Steps From Hell and the music they produce is pretty epic, their bests songs are probably; Birth of A Hero, Earth Rising, To Glory, Heart of Courage, Protectors of The Earth, Archangel and The Last Stand.
Hope  this helps

I have a  few songs, there probably taken but what the heck 

ION - Why


ION - Deeper                  

Seether - Fake it

Celldweller - Eon   

Blessthefall - Whats left of me

Authority zero - New Pollution        

Sorry about the box thing i clicked  it by accident, Hope you liked them

Ideally I will look through some of these this weekend. I doubt I will get through them all though because iv let it build up way too much.

Sorry for the time to reply

happiness7 :
Sunrise and the radioactive cover were good.
2*400 = 800, rounded to 1000 for the links

maguc :
Added 2 by sonata. Style reminds me of Allen Lande
2*400 = 800

PIK412 :
Got the disturbed ones.
Really like hard to see, very good song.
Got paint it black
Dio and iron maiden dont do much for me. They are decent but none of their songs jump out at me.
Got alive, not wild on even flow.
Actively dislike most of slipknots songs.
I'll give 600 because, I really liked hard to see.

MattyIce :
I think I have pretty much every billy talent song. I added them all prior to seeing them live.
I also have the lostprophets song, but given that the singer was done for raping kids, I wouldnt add any of their songs anymore.
Got the offspring ones, and seether, three days grace.
All good suggestions but I have them.
Trivia fact, I'v seen about half of those bands live now.

Popeye116 :
1st was only one I didnt have, was decent. I will need to look at 5 finger death punch, I only have 1 song by them (not including the one suggested above) and they seem pretty good.
400 vizz.

Concretewarrior :
I like their lyrics, well thought out.
got the sick pupies one and not mad about 30 seconds to mars
I'v never heard of 12 stones before, they seem good though.
I added 6 of their suggested songs
6*400 = 2,400, rounded to 3000 for new band.

r0bntina :
added the 2 five finger songs I didnt have. good songs.
2*400, rounded up 1000 vizz.

I may or may not work on from page 9 tomorrow, depending on how busy I am (wow, there are 9 pages, how did that happen).

ghostfishy :
I added 7 songs (by taking dawn and red).
7 * 400 = 2800, round to 3000 for new band.

I'll continue from there later. Either during the week or next weekend.

I typically listen to hard rock, but occasionally like to mix in some other stuff. I’ll start with some of the bands
on your list, and then I’ll add some possibly new ones for you.

Avenged Sevenfold – Hail to the king, Heretic, St. James, Buried alive, Welcome to the family, Almost easy, Afterlife, Critical acclaim, Scream, Dear God, Beast and the harlot, Bat country, Seize the day, Unholy confessions, To end the rapture, Epic of time wasted, Carry on
(My favorite band, so I felt the need to recommend all the must have songs)

Bullet for my Valentine – Saints & sinners, Not invincible, Your betrayal, Scream aim fire, All these things I hate
 
Five Finger Death Punch – Battleborn, Let this go, The house of the rising sun, Wrong side of heaven, Lift me up, Under and over it, The pride, Remember everything, Bad company, War is the answer, The bleeding, Death before dishonor, Stranger than fiction, Never enough

Hollywood Undead – Undead, No. 5, Everywhere I go, The kids

Seether – Same damn life, Words as weapons, Weak, Here and now, Country song, Tonight, Pass slowly, Breakdown, Rise above
this, Remedy, Truth, The gift, Gasoline, Broken, Careless whisper, Seether

Sevendust – Prodigal son, Heart in your hands, Ugly, Suffocate

Atreyu – Honor, Becoming the bull, Bleeding mascara, The crimson

Nonpoint – Breaking skin, That day, Miracle, Frontlines, Bullet with a name, Alive and kicking, Rabia, In the air tonight, Circles, What a day

Godsmack – I stand alone, Serenity, Voodoo, Love-hate-sex-pain, Whiskey hangover, Bad religion, Crying like a b****, Running blind, The enemy, Shine down, Straight out of line,

Shinedown – Bully, Devour, Sound of madness, Second chance, The crow and the butterfly, If you only knew, Save me, I dare you, Burning bright, 45, Diamond eyes

Red – Fight inside, Death of me, Breathe into me

Blue October – Calling you, Hate me, Into the ocean

Stone Sour – Tired, Inhale, Bother, Through glass

Volbeat – Heaven nor hell, A warrior’s call, The hangman’s body count, Lola montez 

In This Moment – Adrenalize, Blood, Whore

All That Remains – What if I was nothing, Two weeks, This calling, The last time

Disturbed – Another way to die, Inside the fire, Stricken, Land of confusion, 10000 fists, Down with the sickness, Prayer

Drowning Pool – Bodies, Turn so cold, Tear away, Sinner, 37 stitches

Chevelle – Hats off to the bull, The clincher, Jars, Well enough alone

Cavo – Thick as thieves, Circles, Champagne

I have a lot more but I figured it would be a little overwhelming, so I might post them later after you've had a chance to listen to some of the other music I listed.

Black and Yellow - Wiz Khalifa 
Coming Down - Five Finger Death Punch 
Coming Home - Diddy 
Doomsday - Nero 
Evil Angel - Breaking Benjamin 
Jungle 0- X Ambassadors 
My Songs Know What You Did In The Dark  ( Light Em Up ) - Fall OUt Boys