Not counting classical or film scores:
Rush - Tom Sawyer, YYZ
Yes - Roundabout, Siberian Khatru, Close to the Edge, Owner of a Lonely Heart, Leave It
Taylor Swift - Style, Look What You Made Me Do
Demi Lovato - Confident
Carly Rae Jepsen - Cut to the Feeling, Run Away With Me
Diablo Swing Orchestra - The Age of Vulture Culture, Jigsaw Hustle, Voodoo Mon Amour, A Tap Dancer's Dilemma, Balrog Boogie, etc.
Dream Theater - Octavarium, The Count of Tuscany, On the Backs of Angels, Bridges in the Sky, Lost Not Forgotten, A Nightmare to Remember, The Shattered Fortress, The Best of Times, The Dark Eternal Night, Panic Attack, Stream of Consciousness, This Dying Soul, etc.
Judas Priest - Painkiller
Snarky Puppy - Tio Maccaco
Gojira - Stranded, Silvera, L'Enfant Sauvage
Juno Reactor - Navras, War Dogs, Pistolero
Nightwish - Creek Mary's Blood, The Greatest Show on Earth, Dead to the World, Dark Chest of Wonders
Epica - The Holographic Principle, The Essence of Silence
Ayreon - Everybody Dies, Day 11: Love, Day 16: Loser, Run Apocalypse! Run!, River of Time
Camel - Freefall, Lady Fantasy
ELP - Tarkus
Ne Obliviscaris - And Plague Flowers the Kaleidoscope
Haken - Streams
Lapsley - Operator
ABBA - Voulez Vous, Mamma Mia, Dancing Queen, Gimme Gimme Gimme! A Man After Midnight, Money Money Money, Does Your Mother Know, etc.
Adele - Rolling in the Deep, Rumour Has It, I Miss You, Skyfall
The Algorithm - Trojans
Alice in Chains - Man in the Box, Phantom Limb, Stone
Alter Bridge - Blackbird, One by One
The Anchoress - What Goes Around, One for Sorrow
Animals as Leaders - CAFO
Anneke van Giersbergen - Drive
ARK - Just a Little
Unitopia - The Garden
Blind Guardian - Fly
Between the Buried and Me - Memory Palace
Pink Floyd - Shine On You Crazy Diamond, Money
Incubus - Pendulous Threads, Anna Molly, Southern Girl, Drive, Beware! Criminal, Love Hurts, Absolution Calling, Follow (1st Movement of the Odyssey), When it Comes, Clean, etc.
Muse - Survival, Supremacy, Panic Station, Take a Bow, Hoodoo, Stockholm Syndrome, Hysteria, City of Delusion, Uprising, United States of Eurasia, The Globalist, Reapers, Citizen Erased, Space Dementia, etc.
That's all I can be bothered to list right now. There's just so many songs with really, really good intros...