In one of the retroclones (Labyrinth Lord, if I recall correctly,) characters with a very low Intelligence score are illiterate. This may be true in B/X or BECMI as well; I never read those versions of Basic, just Holmes. That approach doesn't sit well with me, since I prefer no minimum scores for the base classes; illiteracy is a background option, not a side-effect of a low ability score.
But I do like the idea of having some effect on literacy for low ability scores. Here's an idea: Intelligence 8 and below means a character's lips move while reading, with 5 or less meaning the character reads allowed. This mainly affects the use of scrolls: a magic-user of average or better Intelligence can cast Read Magic and identify the spells on one or more scrolls without problem, but those of low Intelligence have a 1 in 6 chance of casting the spell on the scroll, or 2 in 6 for those of very low Intelligence.
There's also a 1 in 6 chance that reading a normal inscription aloud will alert a nearby monster, spoiling surprise.