This famous song had lyrics by Jack Norworth (1879-1959) and
music by Albert Von Tilzer (1878-1956)
The story goes that Norworth wrote his lyrics after seeing a sign that read:
"Baseball Today - Polo Grounds"
He then gave his lyrics to Albert Von Tilzer who set it to music. The song was copyrighted on May 2, 1908. The song was first sung by Jack Norworth's wife, Nora Bayes. He later wrote different verses for the song in 1927.
Vintage Recordings
One of the first recordings of the song was made in October of 1908 by Edison's National Phonograph Company.
The song is actually in waltz tempo and was sung by Edison staff announcer, Edward Meeker.
You can hear this rare cylinder recording at this link:
"Take Me Out To The Ball Game"
There was a recording made by songwriter Albert Von Tilzer singing "Take Me Out to the Ball Game" with the original 1908 lyrics at a special ASCAP concert in San Francisco
available on this CD set:

Carousel of American Music: The Fabled 24 September 1940 San Francisco Concerts
Modern Recordings
"In selecting the musical tracks we have tried to capture the essence of our film series, to recapitulate and distill the progression from traditional folk music to 1990's rock and roll that the film celebrates, and to honor two of our country's treasures -- our music and our national game." -- Ken Burns and Lynn Novick
From the acclaimed PBS TV series is this CD with numerous versions
of "Take Me Out to the Ballgame":

BASEBALL: A Film by Ken Burns - Original Soundtrack Recording
Hollywood Musical
There was a popular 1949 MGM musical using the 1927 lyrics by Norworth
starring Esther Williams, Gene Kelly and Frank Sinatra with the same song title:



TAKE ME OUT TO THE BALL GAME (2000 DVD)
TAKE ME OUT TO THE BALL GAME (2008 DVD)
About the Song
You can read the background about the song in this recommended new book:

Baseball's Greatest Hit: The Story of Take Me Out to the Ball Game
by Robert Thompson, Tim Wiles, Andy Strasberg
Read more about this song at
The National Baseball Hall of Fame & Museum