What's a contrafact? "In jazz, a melody built upon the chord progression of another piece (after contrafactum, in medieval and Renaissance music." - Grove Music Online (Oxford Music Online)
Many bebop and other types of contrafacts are based on very popular tunes from earlier eras. If you're developing jazz repertoire, it's a good idea to learn the original melodies as well as the contrafact compositions.
The most famous example is the entire genre we call "rhythm changes". These are all contrafacts on Gershwin's "I Got Rhythm." There are hundreds of examples.
To get started, check out this useful little list of jazz contrafacts from Wikipedia.
For example, Dizzy Gillespie's "Groovin' High" is based on Vincent Rose's "Whispering. There are scores of others. Check them out!
Some YouTube clips...
Here's a classic performance of "Groovin' High" by Charlie Parker and Gillespie in 1945. Here's "Whispering" from Red Nichols and His Five Pennies in 1928. A beautiful vocal version of "Whispering" from Harry Belafonte. And a twangy and fun instrumental of "Whispering" from Les Paul and Mary Ford in 1951. Top it off with a quodlibet of "Groovin' High" and "Whispering" together with Phil Woods, Frank Wess, and Jon Faddis with the Barcelona Big Band. (And what's a quodlibet? You can look that one up yourself! :-)