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Benquo comments on Procedural Knowledge Gaps - Less Wrong
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You could memorize the numeric values of the letters (A=1, B=2, ... , Z=26); if you can figure out which number is bigger without counting, you can figure out which letter is later.
Disclaimer: I have not actually done this, because memorizing 26 separate, individually useless items is a pain.
I did this a few years back while bored at school, and it has actually been surprisingly useful.
I find the easiest and quickest way is to try to write the number in a way that makes it look like the letter; eg for H imagine drawing two lines above and below to make it look like an LCD 8. Using this I thoroughly memorized the letters' numbers in about 15 minutes. You'd need to periodically rememorize to keep the numbers fresh, though.
Like D Malik, I did this as a kid. I managed to invent modular arithmetic as a game; the big insight for me was that, although I had originally set ‘Z’ = 26, it was also true that ‘Z’ = 0. I suppose that it was doing these arithmetic problems (for fun) that allowed me to actually complete the memorisation.
After deciding that counting should begin with 0, I've tried to relearn them, but it didn't take (it's easier to just add or subtract 1).