The reason its not alphabetical is a matter of historical development of spectral classifications. James Kaler does a nice job of describing it in his book "The Stars and their Spectra".

Basically, stellar spectra were initially classified and had many more letters than the current sequence. Annie Jump Cannon is due a lot of credit for the current spectral sequence. The original ordering was based upon the strength of the hydrogen lines with A the strongest and O the weakest. Then it was realized that some spectral classes needed to be dropped (such as the original E and H). The result is OBAFGKM.

The reason O and B end up before A is that they have stronger helium lines but weaker hydrogen lines than A so they fit before A. The rest of the spectral classes actually do increase with the alphabet - and show corresponding changes in spectral lines - weakening hydrogen lines, increasing strength of metal lines and even molecule lines in the M-class stars.

Perhaps not pretty, but there are cute ways of remembering it:

"Oh Be A Fine Girl/Guy Kiss Me" and so on.