Here is a list I've compiled of movies where people sing in cars. Please feel free to add to it. The only requirement is that characters must be driving in the car while the singing is taking place. The question marks represent unknown song titles/artists.

Movie Actor(s) Artist Song

Say Anything - John Mahoney - Steely Dan - Rikki Don’t Lose That Number
Men In Black - Tommy Lee Jones - Elvis Presley - The Promised Land
How to Make an American Quilt - Several - Neil Diamond - Sweet Caroline
Pulp Fiction - Bruce Willis - The Statler Brothers - Flowers On The Wall
Wayne’s World - Mike Myers/Dana Carvey - Queen - Bohemian Rhapsody
Jerry Maguire - Tom Cruise - Tom Petty - Free Fallin’
Almost Famous - Several - Elton John - Tiny Dancer
Thelma and Louise - Geena Davis/Susan Sarandon - ? - ?
Chitty Chitty, Bang Bang - D. VanDyke/Sally Howes - ? - Chitty Chitty Bang Bang
Haunted Honeymoon - Gene Wilder/Gilda Radner - ? - ?
Grease - Olivia N. John/J. Travolta - ? - We Go Together
Tommy Boy - Chris Farley/David Spade - The Carpenters - Super Star
Twilight Zone Movie - ? - CCR -Midnight Special
Rain Man - Tom Cruise - ? - ?
O Brother, Where Are Thou? - Several - ? - ?
Stepmom - Julia Roberts/Kids - Marvin Gaye/Tammi Terrell - Ain’t No Mountain
Crossroads - Britney Spears/Others - N’sync - Bye, Bye, Bye
Bad Boys - Wil Smith/Martin Lawrence - Inner Circle - Bad Boys
Planes, Trains & Automobiles - John Candy/Steve Martin - ? - Blue Moon Over Kentucky/The Flintstones Theme
Rush Hour 2 - Jackie Chan/Chris Tucker - Beach Boys/War - California Girls/Edwin Starr
American Beauty - Kevin Spacey - American Woman - The Guess Who
The Money Pit - Joe Mantenga - Al Martino - I’ve Got To Be Me
At Long Last, Love - Several - Cole Porter - Friendship
The Coneheads - Dan Ackroyd/Jane Curtain - Soft Cell - Tainted Love
A Night at the Roxbury - Will Farrell/Chris Kattan - ? - Baby Don’t Hurt Me No More
Lilies of the Field - Sydney Poitier - ? - Amen
Tie Me Up, Tie Me Down - Antonio Banderas - ? - ?
A Christmas Story - Several - Traditional - Jingle Bells
Sleepless in Seattle - Tom Hanks/Meg Ryan - Traditional - Jingle Bells
Meet the Parents - Robert DeNiro - Peter, Paul & Mary - Puff the Magic Dragon
American History X - Ethan Suplee - ? - The White Man Marches On
The Sweetest Thing - Christina Applegate/C. Diaz - Rupert Jones - Escape (The Pina Colada Song)
Harold & Kumar go to White Castle - Harold & Kumar - Wilson Phillips - Hold On