The New York Yankees were the first team to begin regularly wearing uniform numbers. A tradition dating back to 1929. Other teams before 1929 tried putting numbers on their uniforms, but mostly on an experimental only basis, usually not lasting longer than a season or sometimes even past a few games.  The Yankees were the first to implement uniform numbers and maintain the practice indefinitely.

This website attempts to make it easy to find who wore what numbers in what year since they began wearing numbers in 1929.  It's not 100% complete, so if there's any information you can help with, please feel free to contact me to fill in the blanks.