Hello Stranger - Barbara Lewis
Help Me - Joni Mitchell
Honky Cat - Elton John
Haven’t Got Time for the Pain - Carly Simon
Here Comes the Rain Again - Eurythmics
Alternate: Have You Seen Her - The Chi-Lites
Here Come the Warm Jets - Eno
Hay - Butthole Surfers
(22 going on 23 backwards at high speed)
Haunted When the Minutes Drag - Love and Rockets
Hope - Bauhaus
Hong Kong Garden - Siouxsie and the Banshees
Alternate:
Ha Ha Ha - Flipper
I have a few more, but I can’t leave this one out.
Happy Trails - Roy Rogers, Dale Evans & The Pioneers
Heartbreaker - Led Zeppelin
Happy Heart - Petula Clark
He Doesn’t Know Why - Fleet Foxes
Heads Will Roll - Yeah Yeah Yeahs
Hey Nineteen - Steely Dan
Holiday - Green Day
Almost 40 years of listening to this album, and I never noticed. What a maroon. 
Late to the party again!
A Hard Rain’s A-Gonna Fall - Bob Dylan
Help Me Make It Through The Night - Gladys Knight And The Pips
Hello, I Love You - The Doors
Hey Boy, Hey Girl - The Chemical Brothers
Hotel Chambermaid - Graham Parker And The Rumour
Alternate: House Of The Rising Sun - John Otway
Have a watch and laugh yourself sick.
j
Heheh, in your defense they do move the faders around a lot.
Happy Phantom - Tori Amos
He Ain’t Heavy, He’s My Brother - The Hollies
Heart-Shaped Box - Nirvana
He Makes You Look Fat - Nick Helm
Horseshoes - Moxy Fruvous
Alternate: Hallelujah - Jeff Buckley
What are your favorite H songs? POLL 1 of 4. Select up to 9 from this list.
- Ha Ha Said the Clown – Manfred Mann
- Hackensack – Fountains of Wayne
- Hair of the Dog – Nazareth
- Haiti – Kid Creole & the Coconuts
- Haitian Divorce – Steely Dan
- Hallelujah – Bram Wijnands
- Hallelujah I Love Her So – Ray Charles
- Hand in My Pocket – Alanis Morissette
- Handbags and Gladrags – Rod Stewart
- Handle With Care – Traveling Wilburys
- Handyman – James Taylor
- Hangin’ Round – Lou Reed
- Hanging Garden, The – The Cure
- Happening, The – The Supremes
- Happiness is a Warm Gun – The Beatles
- Happy – Pharrell Williams
- Happy Heart – Petula Clark
- Happy House – Siouxsie & the Banshees
- Happy Jack – The Who
- Happy Phantom – Tori Amos
- Happy Together – The Turrtles
- Happy Trails – Roy Rogers, Dale Evans & the Pioneers
- Happy Unhappy – The Beths
- Harborcoat – R.E.M.
- Hard Day’s Night, A – The Beatles
- Hard Rain’s A-Gonna Fall, A – Bob Dylan
- Hard Sun – Eddie Vedder
- Harvest Moon – Neil Young
- Harvester of Sorrow - Metallica
- hate to be lame – Lizzy McAlpine feat. FINNEAS
- Haunted When the Minutes Drag – Love & Rockets
- Have a Cigar – Pink Floyd
- Have You Ever Seen the Rain – Creedence Clearwater Revival
- Have Yourself a Merry Little Christmas – Judy Garland
- Haven’t Got Time for the Pain – Carly Simon
- Hawaiian Roller Coaster Ride – Mark Keali’I Ho’omalu
- Hay – Butthole Surfers
- Hazy Shade of Winter – Simon & Garfunkel
- Hazy Shade of Winter – The Bangles
- He Ain’t Heavy, He’s My Brother – The Hollies
- He Doesn’t Know Why – Fleet Foxes
- He Makes You Look Fat – Nick Helm
- He Went to Paris – Jimmy Buffett
- Head Over Feet – Alanis Morisette
0
voters
What are your favorite H songs? POLL 2 of 4. Select up to 9 from this list.
- Head Over Heels – Tears for Fears
- Headline News – “Weird Al” Yankovic
- Heads Will Roll – Yeah Yeah Yeahs
- Healingbow – Eden
- Heard It in a Love Song – The Marshall Tucker Band
- Heart and Soul – Huey Lewis & the News
- Heart and Soul – Joy Division
- Heart Heart Head – Meg Myers
- Heart it Races – Dr. Dog
- Heart Like a Wheel – Linda Ronstadt
- Heart of Glass - Blondie
- Heart of Gold – Neil Young
- Heart of Mine – Bob Dylan
- Heart of the Matter, The – Don Henley
- Heartbreaker – Led Zeppelin
- Heart-Shaped Box – Nirvana
- Heat of the Moment – Asia
- Heaven (Must be There) – Eurogliders
- Heaven is a Place on Earth – Belinda Carlisle
- Heavy Metal – Don Felder
- Helen Wheels – Paul McCartney & Wings
- Hell – Squirrel Nut Zippers
- Hell’s Bells – AC/DC
- Hello - Adele
- Hello – Lionel Richie
- Hello Stranger – Barbara Lewis
- Hello Stranger – Emmylou Harris
- Hello, I Love You – The Doors
- Help Me – Joni Mitchell
- Help Me Make It Through the Night – Gladys Knight & the Pips
- Help Me, Rhonda – The Beach Boys
- Help! – The Beatles
- Helpless – Neil Young
- Helter Skelter – The Beatles
- Helvegen – Wardruna & Aurora
- Here Come the Warm Jets – Eno
- Here Comes a Savior – The Living Tombstone
- Here Comes the Rain Again - Eurythmics
- Here Comes the Sun – The Beatles
- Here Comes Your Man – Pixies
- Here You Come Again – Dolly Parton
- Here, There & Everywhere – The Beatles
- Here’s That Rainy Day – Astrud Gilberto
- Heroin – The Velvet Underground
0
voters
What are your favorite H songs? POLL 3 of 4. Select up to 9 from this list.
- Heroin Girl – Everclear
- Hey Boy, Hey Girl – The Chemical Brothers
- Hey Bulldog – The Beatles
- Hey Hey, My My (Into the Black) – Neil Young & Crazy Horse
- Hey Joe – Jimi Hendrix Experience
- Hey Jude – The Beatles
- Hey Jupiter – Tori Amos
- Hey Nineteen – Steely Dan
- Hey Now – WiL
- Hey Porter – Johnny Cash
- Hey Ya - Outcast
- Hickory Wind – Gram Parsons & Emmylou Harris
- Hide in Your Shell – Supertramp
- Hide the Beer, the Pastor’s Here – The Swirling Eddies
- High Five – Sigrid
- High Flying Bird – Elton John
- Higher Ground – Red Hot Chili Peppers
- Higher Ground – Stevie Wonder
- Highway 61 Revisited – Bob Dylan
- Highway of Heroes – The Trews
- Highway Patrolman – Bruce Springsteen
- Highway Star – Deep Purple
- Highway to Hell – AC/DC
- Hips Don’t Lie – Shakira
- Hit Me With Your Best Shot – Pat Benatar
- Hit Me With Your Rhythm Stick – Ian Dury & the Blockheads
- Hit The Road Jack – Ray Charles
- Hocus Pocus – Focus
- Hold Me – Fleetwood Mac
- Hold Me Now – Thompson Twins
- Hold My Life – The Replacements
- Hold On – Ian Gomm
- Hold On, I’m Coming – Sam & Dave
- Hold the Line – Toto
- Hold Your Head Up – Argent
- Holiday – Green Day
- Holiday in Waikiki – The Kinks
- Holiday Road – Lindsay Buckingham
- Holidays in the Sun – Sex Pisols
- Hollywood Dream – Thunderclap Newman
- Hollywood Swinging – Kool & the Gang
- Holy Diver - Dio
- Holy, Holy, Holy, Lord God Almighty – Vienna Boys Choir
- Home Again – Carole King
0
voters
What are your favorite H songs? POLL 4 of 4. Select up to 9 from this list.
- Home by the Sea – Genesis
- Home Sweet Home – Motley Crue
- Homegrown Tomatoes – Guy Clark
- Homeward Bound – Simon & Garfunkel
- Homework – Fleetwood Mac
- Honesty – Billy Joel
- Hong Kong Garden – Siouxsie & the Banshees
- Honky Cat – Elton John
- Honky Tonk Women – The Rolling Stones
- Hope – Bauhaus
- Hora Decubitus – Charles Mingus
- Horseshoes – Moxy Fruvous
- Host of Seraphim – Dead Can Dance
- Hot for Teacher – Van Halen
- Hot Fun in the Summertime – Sly & the Family Stone
- Hot in the Ciy – Billy Idol
- Hot Night – Laura Branigan
- Hot Nite in Dallas – Moon Martin
- Hot Rod Lincoln – Commander Cody & His Lost Planet Airmen
- Hotel California – Eagles
- Hotel Chambermaid – Graham Parker & the Rumour
- Hotel Womb – The Church
- Hourglass – Squeeze
- House of Bamboo – Southern Culture on the Skids
- House of the Rising Sun – The Animals
- Houses of the Holy – Led Zeppelin
- How Can I Miss You When You Won’t Go Away? – Dan Hicks & His Hot Licks
- How Deep is Your Love – Bee Gees
- How Do You Do – Boom
- How Do You Do! – Roxette
- How Far I’ll Go – Auli’i Cravalho
- How High the Moon – Les Paul & Mary Ford
- How Long – Tove Lo
- How Soon Is Now – The Smiths
- How Sweet It Is to Be Loved by You – Marvin Gaye
- Hunger Strike – Temple of the Dog
- Hungry – Paul Revere & the Raiders
- Hungry Freaks, Daddy – Mothers of Invention
- Hunter – Dido
- Hurricane – Bob Dylan
- Hurt – Johnny Cash
- Hypnotize – The Notorious B.I.G.
- Hypnotized – Fleetwood Mac
0
voters
The Missing (from my list):
Have I Told You Lately - Van Morrison
Having a Party - Sam Cooke
Hello In There - John Prine 
Highwayman - The Highwaymen
Hungry Eyes - Merle Haggard
He Stopped Loving Her Today - George Jones
He’s A Rebel - The Crystals
Highway Patrol - Junior Brown
The rest from my list:
Heartbreak Hotel - Elvis Presley (a surprising omission)
Hear My Train A-Coming - The Jimi Hendrix Experience
Here She Comes Now - Velvet Underground
Hand In Glove - The Smiths
Hearts On Fire - Gram Parsons and Emmylou Harris
The Healer - John Lee Hooker
Hokey Pokey - Richard and Linda Thompson
Hungry Heart - Bruce Springsteen
More from me:
Hammond Song - The Roches
Hang On Little Tomato - Pink Martini
Happy Boy - The Beat Farmers
Happy Hour - The Housemartins
Harder, Better, Faster, Stronger - Daft Punk
Hartlepool - Boothby Graffoe
Hayloft - Mother Mother
He’ll Have To Go - Jim Reeves
Hell Hound On My Trail - Robert Johnson
Hello! - Cast of The Book of Mormon
Hello…I’m Johnny Cash - Alabama 3
He Loves Me - Jill Scott
Here Comes The Hotstepper - Ini Kamoze
Here Come The Girls - Ernie K Doe
Hernando’s Hideaway - The Johnston Brothers
Hey Eugene! - Pink Martini
High - Lighthouse Family
His Eye Is On The Sparrow - Mahalia Jackson
History Repeating - Propellerheads w. Shirley Bassey
Hit or Miss - Odetta
Hit That Perfect Beat - Bronski Beat
The Holly And The Ivy - Magpie Lane
Hooked On A Feeling - Blue Swede (OOGA CHAKA OOGA OOGA)
A Horse With No Name - America
Hot Knife - Fiona Apple
Hound Dog - Big Mama Thornton (sorry Elvis!)
The House Is Rockin’ - The Brian Setzer Orchestra
House of Fun - Madness
How Bad Can I be? - Ed Helms (from The Lorax)
How Could Red Riding Hood - The Yacht Club Boys
How Could You Believe Me? - Mandy Patinkin
How Do I Live - LeAnn Rimes
Hurt - Eric Whitacre
Hyperactive! - Thomas Dolby
Whenever I see the Pistols’ Holidays in the Sun I automatically think of The Dead Kennedy’s Holiday in Cambodia.
More soundalikes, reminders, or quasi-copies which aren’t covers:
Hallelujah – Bram Wijnands ==> Halleluhwah - Can
Happy – Pharrell Williams ==> Happy? - Public Image, Ltd.
Heads Will Roll - Yeah Yeah Yeahs ==> Heads Will Roll - Echo and the Bunnymen
I do see that I and MrDibble are still keeping all of these punk & post-punk acts from getting shut out tho.
Now just the criminally ignored:
Hounds of Love - Kate Bush
Hiroshima Mon Amour - Ultravox
Hands Across The Ocean - The Mission
Not Hasa Diga Ebowai?