Songs featuring "heart" in the title

A few that aren't present here (not sure if you're counting songs with "hearts" in the title):

How Can You Mend A Broken Heart - Al Green
Here In My Heart - Al Martino
Half A Heart - Barenaked Ladies
Break Your Heart - Barenaked Ladies
Hungry Heart - Bruce Springsteen
Two Hearts - Bruce Springsteen
Straight from the Heart - Bryan Adams
Hearts of Fire - Bryan Adams
Young Hearts Run Free - Candi Staton
Don't Go Breaking My Heart - Elton John & Kiki Dee
A Good Heart - Feargal Sharkey
Piece of My Heart - Janis Joplin
You Stole The Sun From My Heart - Manic Street Preachers
Heart of Lothian - Marillion
Stop Cryin' Your Heart Out - Oasis
Your Cheatin' Heart - Patsy Cline
This Heart Will Love Again - Steps
Stop Draggin' My Heart Around - Stevie Nicks and Tom Petty
Listen to Her Heart - Tom Petty & the Heartbreakers

I have a few (apologies if any have been repeated):

How Can You Mend A Broken Heart? - Bee Gees
Heart Full of Soul - The Yardbirds
Two Hearts - Phil Collins (don't know if either of these are the same song as the ones you have above but I'm pretty sure they pre-date them)
You Have Placed A Chill In My Heart - Eurthymics
Wooden Heart - Elvis Presley
Heartbreak Hotel - Elvis Presley
Anyone Who Had A Heart - Cilla Black
There Must Be An Angel (Playing With My Heart) - Eurythmics (again)
Something's Gotten Hold Of My Heart - Gene Pitney
(also later recorded by Marc Almond, with Gene Pitney)
Hand On Your Heart - Kylie Minogue
Young at Heart - the Bluebells
Queen of my Heart - Westlife
Thunder In My Heart - Leo Sayer
My Heart Has A Mind of its Own - Connie Francis
Don't Break The Heart That Loves You - Connie Francis (again)
Let the Heartaches Begin - Long John Baldry
When The Heartache Is Over - Tina Turner
Heartache Tonight - The Eagles
Heart of Gold - Neil Young
Owner of a Lonely Heart - Yes
Open Your Heart - Madonna
Young Hearts Run Free - Candi Staton
Heartbreaker - Dionne Warwick
Every Beat of My Heart - Rod Stewart
Heartbeat - Buddy Holly (as covered by Showaddywaddy and of course, Nick Berry who starred and sang the theme tune of the Sunday night programme of the same name)
Heart of Stone - Suzi Quatro
Heart of Stone - Bucks Fizz
Heart over Mind - Kim Wilde
The Heart of a Man - Frankie Vaughan
Heart and Soul - T'Pau
Heart - Pet Shop Boys
Zing Went The Strings Of My Heart - I don't actually know who did this one.

A couple more:

Sheer Heart Attack - Queen
and of course - Sgt. Pepper's Lonely Hearts Club Band - The Beatles

You Made Me the Thief of your Heart - Sinead O'Connor
Heart-Shaped Box - Nirvana

L.S.G - Hearts

Ramones - Listen to My Heart

My Heart, Your Hands - From First to Last; Try Sleeping with a Broken Heart - Alicia Keys; Cross My Heart - The Rocket Summer; Hearts Burst into Fire - Bullet for My Valentine; Listen to Your Heart - DHT (i think its a remake); Jar of Hearts - Christina Perri; Heartbreaker - Led Zeppelin; Hell on the Heart - Eric Church; Heartless - Kanye West; America's Suitehearts - Fall Out Boy; Broken Hearts, Torn Up Letters and the Story of a Lonely Girl - Lostprophets; Heart in a Blender - Eve 6; Half of My Heart - John Mayer and Taylor Swift; The Coldest Heart - The Classic Crime; Beating Hearts Baby - Head Automatica; Confessions of a Broken Heart - Lindsay Lohan; Break Your Little Heart - All Time Low; Break Your Heart - Ludacris and Taio Cruz; All Hail the Heartbreaker - The Spill Canvas; The Damage in Your Heart - Weezer; Heart of Worship - many different artists; My Heart - Paramore; 6th Avenue Heartache - The Wallflowers; Words Hands Hearts - Yellowcard; Breaking Your Heart - Cheyenne Kimball; Quit Breaking My Heart - Mandy Moore; Until Her Heart Stops - Hawthorne Heights; You Be The Anchor That Keeps My Feet On The Ground, I'll Be The Wings That Keep Your Heart In The Clouds - Mayday Parade; Unchain My Heart - Joe Cocker; The Heart Brings You Back - Blues Traveler (but i've also seen it called Hook too, so i'm not sure about that one)

sorry if there are repeats, that's just everything in my library. hope it helps!

Just for anyone searching for varients on "heart" (like i was when i came across this great website) here are a few more.
(i have found quite a lot of old 30's and 40's jazz songs too, not included here but i can do if you want

Fats Domino - There Goes My Heart
Frankie Avalon - Just Ask Your Heart
Bob Dylan - Lily, Rosemary and the Jack of Heart(s)
Joni Mitchell - If I Had a Heart
Neil Young - Only Love Can Break Your Heart
Pink Floyd - Set The Controls For The Heart Of The Sun
Pink Floyd - Atom Heart Mother Suite
Queen - Sheer Heart Attack
Roxy Music - In Every Dream Home A Heartache
Dexy's Midnight Runners - Breaking Down The Walls Of Heartache
Florence & tHe Machine - Rabbit Heart (Raise It Up)
Ella Fitzgerald - Heart And Soul
Fleetwood Mac - My Heart Beat Like A Hammer
Frank Sinatra - Young At Heart
Patsy Cline - Your Cheatin' Heart
Psychedelic Furs - Heartbeat
Rolling Stones - Heart Of Stone
Dionne Warwick - Anyone Who Had A Heart
Dusty Springfield - Anyone Who Had A Heart (same)
Tony Bennett - I Left My Heart In San Francisco
Jimmy Ruffin - What Becomes of the Broken Hearted
Aztec Camera - Somewhere In My Heart
Roxette - Listen To Your Heart
Maisonettes - Heartache Avenue
Alvino Ray Orchestra - Deep In The Heart Of Texas
Undertones - A Good Heart
Yeah Yeah Yeahs - Cheated Hearts
Tony Braxton - Unbreak My Heart
Flirtations - Nothing BUt A Heartache

Mastodon - Hearts Alive
Killswitch Engage - The End of Heartache
Stone Temple Pilots - Trippin' on a Hole in a Paper Heart

Marty Balin - Hearts