Alignment languages? Yeah. Let's talk about them. A few days ago, Noisms was talking about making them the secret codes/handshakes of Illuminati style secret societies as a way to justify them and use them to add conflict to a setting. I've got another take, although sorta similar.
So Gygax likens alignment languages to ecclesiastical Latin, but then tries to limit their usefulness to just checking to see if the monsters are really on your side or not, and maybe getting them to help out against some monster of another alignment.
I think in my games from now on, I'll keep the "ecclesiastical Latin" idea and ditch the rest. Alignment languages will be specific dead languages in the campaign world. They're not secret. They're not exclusive. They're not even really designed to be used as a secret code language or shibboleth. But whatever alignment you choose determines which of the three (luckily for me, I run Classic D&D with Law-Neutrality-Chaos only) your PC knows, in addition to Common and any demi-human languages.
Characters with high Int scores can choose to learn one of the other Alignment languages (or both if their Int is high enough). This means you can't necessarily trust someone just because they happen to speak Ancient Gardelish and so do you (not that you should implicitly trust someone of your own alignment anyway, even if you're both Lawful). It also gives a reason why adventuring parties might actually WANT a range of alignments in the party. Jerrash the Wildling may be able to translate those inscriptions written on the black pit's rim in Albondish, while Stoutheart Aleena can read the holy scrolls written in Zebrionic, and Torgo the Uncommitted can negotiate with the centaurs.