The following are by no means all he wrote but I have no space for them all.
Other names are collaborators with words for the music.
Ain't God Good to Indiana 1946
Ain't There Anyone Here for Love? 1953
Amazing What Love Can Do 1940
Any Time at All
April in My Heart 1937..Hoagy Carmichael & Helen Meinardi
At the Garden Gate 1957..Harold McCord
Ballad in Blue 1935..Irving Kahal
Barbara 1957..Hoagy Carmichael
Behold How Beautiful 1961..Stanley Adams
Blue Orchids 1939..Hoagy Carmichael
Boneyard Shuffle 1925..[piano only]
Break it Up Cinderella 1940..Johnny Mercer
Brown County In Autumn 1949
But They Better Not Wait Too Long..Johnny Mercer
Can't Get Indiana Off My Mind 1940..Robert DeLeon
Casanova Cricket 1947..Hoagy Carmichael, Larry Markes & Dick Charles
Chimes of Indiana 1954..Hoagy Carmichael
Close Beside You 1965..Harold Adamson
Clouds 1957..Christina G. Rossetti
College Swing 1938..Frank Loesser
Come Easy Go Easy Love 1931..Sunny Clapp
Comrades 1957..Agnes Louis Dean
The Coronation Queen Waltz.. Hoagy Carmichael
Darn Clever These Chinese 1939..Johnny Mercer
Daybreak 1932..Hoagy Carmichael
Dear Friends and Gentle Hearts 1943..Hoagy Carmichael
Doctor, Lawyer, Indian Chief 1945..Paul Francis Webster
Don't Forget to Say "No" Baby 1941..Hoagy Carmichael, Cee Pee Johnson & Lou Victor
The Doodle Bug Rag 1952..Hoagy Carmichael
Down T'Uncle Bill's 1934..Hoagy Carmichael & Johnny Mercer
Dreams 1957..Marchette Gaylord Chute
Drip Drop 1943..Ray Gilbert
Easter 1957..Ignez Hogan
Everything Happens to Me 1940..Johnny Mercer
Georgia On My Mind 1930..Stuart Gorrell
Grandfather Clock 1957..Fredrick Shummuay Smith
Harvey 1929..Hoagy Carmichael & Irving Mills
He's Dead But He Won't Lie Down 1954..Johnny Mercer
Heart and Soul 1938..Frank Loesser
Heaven Help this Heart of Mine
Hong Kong Blues 1939..Hoagy Carmichael
How Little We Know 1944..Johnny Mercer
How Nice for Me 1939..Johnny Mercer
I Get Along Without You Very Well 1938..Mrs. Jane Brown Thompson
I Guess It Was You All the Time 1953..Johnny Mercer
I'll Dance at Your Wedding 1941..Frank Loesser
I'm Gonna Get Married in the Morning 1946..Hoagy Carmichael
In the Cool, Cool, Cool of the Evening 1951..Johnny Mercer
In the Still of the Night 1932..Jo Trent
Kinda Lonesome 1938..hoagy Carmichael, Leo Robin & Sam Coslow
Lamplighters Serenade 1942..Paul Francis Webster
Lazy River 1931..Hoagy Carmichael & Sidney Arodin
Lazybones 1933..Hoagy Carmichael & Johnny Mercer
Little Old Lady 1936..Hoagy Carmichael & Stanley Adams
Manhattan in the Spring 1940..Hoagy Carmichael, Helen Meinardi & Herb Sanford
Maybe You Know What I Mean 1935..Johnny Mercer
My Resistance is Low 1951..Harold Adamson
The Nearness of You 1937..Ned Washington
The Old Music Master 1943..Johnny Mercer
Ole Buttermilk Sky 1946..Hoagy Carmichael & Jack Brooks
One Morning in May 1933..Mitchell Parish
Poor Old Joe 1932..Hoagy Carmichael
Riverboat Shuffle 1924..Hoagy Carmichael, Dick Voynow, Irving Mills & Mitchell Parish
Rockin' Chair 1929..Hoagy Carmichael
Skylark 1941..Johnny Mercer
Small Fry..Frank Loesser
Stardust 1928..Mitchell Parish
Take Me to Your Heart Again 1948..Hoagy Carmichael, Arthur Swanstorm & Maxon F. Judell
Two Sleepy People 1938..Frank Loesser
Washboard Blues 1925..Hoagy Carmichael, Fred B. Callahan & Irving Mills
Wedding Song 1935..Hoagy Carmichael
Who Killed 'Er (Who Killed the Black Widder) 1947..Hoagy Carmichael, Janice Torre & Fred Spielman
Yabba Dabba Dabba Dabba Do...Hoagy Carmichael
Ballad in Blue 1935..Irving Kahal
Dreams 1957..Marchette Gaylord Chute