We don’t have an alphabet song where I’m from, but I simply remember the list of letters. I’ll just mentally recite “a, b, c, d, e...” very fast. If I need to do figure out what letter’s next after one somewhere in the middle I don’t need to recite all of it from the beginning, but I also don’t immediately recall the next letter; I just start reciting it a bit before, e.g. if you’ll ask me what’s after “N” I’ll do a very quick “m,n,o,p” in my mind and then say “O”. I’m not exactly sure how I pick the starting point, it’s automatic; it seems there are some “fixed” starting points for some reason (that come up often) and I usually pick the nearest one; for instance if you asked me what’s after “o” I’ll also start at “m”. Very rarely it happens that I start with a letter following the reference one, then I’ll stop after a few letters and try again with an earlier stop-point.

Me too, and I seem to have a checkpoint at M too.

(I recite the alphabet mentally in my native language, and I suspect the rhythm of the syllables generates some break-points unconsciously, and they probably differ with language. Though I just tried it and it works in English too, it just seems like it takes a bit more time to “think of” a starting point; I wouldn’t be surprised if my brain did a two-way conversion before I could notice it.)

Fun fact: it takes me much shorter (not much longer than my usual reaction times) to translate the words for ‘left’ and ‘right’ across any two languages I know than to actually tell which side is which -- I have to imagine I'm holding a pen and that's the right hand, which can take as long as one second.

ETA: I just tried singing the song, and I noticed that after H or so I actually have to stop and do it “my way” very fast to remember what’s next. Apparently having to think of the notes (as I said, I’m not used to it sung) is enough to disturb the recall.

No problem at all with the song, but it's still slower than the other way, by about a factor of 2. Also, I don't have checkpoints with the song, I have to start from A. (Well, I have one at W but it's not very useful.)

Also, this seems to be my an automatic method for memorizing lists; I have terrible memory and it’s very hard for me to memorize abstract things like names, numbers and dates, but the few that I do manage—a few phone numbers and the first 25 or so decimals of π—I remember as a quick list of individual digits.

Some strings of numbers I remember as sequences of digits spoken, others as sequences of digits written, others as a series of finger movements I make to type them -- or in certain cases, to play them on a guitar if they were a tablature. (And I remember the digits of pi through the mnemonic “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics”.)