Who invented the stellar classification system 'OBAFGKM'?

The famous spectral sequence of stellar types was developed by Harvard astronomer E.C. Pickering based on an original scheme using the alphabet sequence from A to Q. He used stellar spectra obtained in the 1890's to distinguish stars that had similar spectra. Then, in the early 1900's Henry Draper completed the famous 'Henry Draper Catalog' involving the spectra of over 200,000 stars. This led to the refined Harvard Spectral Sequence of O B A F G K M, as many of Pickering's original classifications were found to be redundant. This was replaced in 1943 by the Morgan, Keenan, and Kellman OBAFGKM sequence with decimal sub-typed such as O4, G5 and M7 based on precise spectral line strength measurements of certain diagnostic indicator lines.

The above figure and more details can be seen at Jesse Allen's page over at NASA/Goddard