You've probably heard it a hundred times, but "Rolling in the Deep" I'm ashamed to admit does make my back shiver. Adele has a really powerful voice.

Some others:

Xanadu - Rush (at least listen until 2:03. That's the part that makes me shiver)

Black Sabbath - Black Sabbath

One Down, Two to Go - King Diamond

The Devil's Triangle - King Crimson (Note: Purely instrumental and very long.)

The Needle and the Damage Done - Neil Young

Pink FLoyd - Comfortably Numb, Time, Wish You Were Here, Money, Us and Them etc.

Rush - La Villa Stragiato, Red Barchetta

King Crimson - Lakes Tongues in Aspic, Starless, Red, Epitaph etc.

Yes - Siberian Khatru, Heart of Sunrise etc.

Guns N Roses - Knocking on Heavens Doorway

The Who - Baba O Riley

Rolling Stones - Ruby Tuesday

Journey - Dont Stop Believin, Anytime, Faithfully, Only Solutions

Lynyrd Skynyrd - Freebird

Dire Straits - Brothers in Arms, Telegraph Road

Bon Jovi - Bed of Roses, Blaze of Glory

Blue Oyster Cult - Burnin For You, Dont Fear the Reaper

Boston - More than a Feeling

Chevelle is a great band related those. Slipknot definitely does it for me, as well, but it doesn't seem like you're looking for that type of band. Another band is Bullet for My Valentine, which has some screaming but they're a great band. Deftones is an AMAZING band, you should definitely check them out.

Seeing as how you're looking for single songs:

All That Remains' "The Waiting One" is a slower song and it's pretty great

Atreyu's "Becoming the Bull"

Bloodsimple's "Out to Get You"

Crossfade's "Cold"

Evanescence's "Going Under" (as well as many other songs)

Evans Blue's "Cold"

Quite a few of Breaking Benjamin's songs does it for me, but I especially like "Diary of Jane"

Flyleaf's "I Can Feel You All Around Me"

For Today's "Fearless" has screaming, but nevertheless it's great

Green Day's "21 Guns"

Hollywood Undead's "Bullet"

In This Moment "Blood" album is filled with amazing songs

Korn has been my addiction lately

Linkin Park's "One Step Closer"

Machine Head's "Darkness Within"

I love "The Black Parade" album by My Chemical Romance

The Offspring's "You're Gonna go Far, Kid"

Pantera's "This Love"

A Perfect Circle and Tool are beyond amazing

Seether, Smashing Pumpkins, Stone Sour, and System of a Down

Three Days Grace has too many great songs to list

Volbeat and 10 Years are great, too

Spinal Menangitis - Ween

Happy Birthday - The Birthday Massacre

I looove your three songsss!!!!!

some songs that make me shiver are kind of old songs

I don't know if you like that

heaven and hell by black sabbath

keep on moving by deep purple

bring it on home by led zeppelin

and

young volcanoes by fall out boy

sick by westbam

the extra by placebo

Haunted by evanescence