Having had my imagination captured at some point by Billboard Year-End charts, I went and found them all, and gathered them for your viewing pleasure. Keep in mind that the list was not always of 100 songs, so here is the breakdown:

1946-1949 Top Songs (no real pattern)
1950-1955 Top 30
1956-1958 Top 50
1959-Now Top 100

Be sure to visit the iTunes Music Store, where you can listen to a 30 second snippet of the song and, if you so desire, buy the song for 99¢.

My gratitude to both Nickyrock and Henry for providing information about 1946-1949. Previously I had only been able to locate unreliable sources for those years, and their combined efforts have lead me to post a set with which I feel comfortable. Again, thanks to both of them.