WAR - Awareness has 2 major uses, and one common use. The first major use is with RI, as mentioned, preventing crits if hit from the back. The biggest caveat of Awareness + RI is that Awareness lasts 15s and RI lasts 20s. This leaves a 5s window where you're vulnerable to being crit, and if you're tanking a bunch of mobs this usually means 5s of non-stop crits. It's actually really good vs bosses, since damage rolls checks crit before parry which means you can still get crit from the front. The second major use is in Deliverance, where a crit will actually do significant damage because you're lacking the +healing, unless you have Thrill + Conv up. I usually pair Awareness with RI or Foresight in Deliverance for most effective use. The common use for Awareness - one all 3 classes benefit from - is in situations where you only have lesser CDs available and the main thing threatening your life is a crit. In this situation, Awareness shines, even if it did nothing at all.

PLD - No reason not to use it. Useful in SwO, during Bulwark w/ multiple mobs, other stuff idk.

DRK - Useful outside of Grit, useful when the only thing threatening your life is a crit.

So. Unless a fight has a high crit rate phase (Shiva, T11) then Awareness is best used when being crit would otherwise kill you. Since the chance of monsters actually critting you is very low, Awareness seems useless and should be popped on CD - but that's not really using Awareness effectively. You can pop Awareness on CD if there's no point where a crit would kill you, but I'll usually hang on to it just incase I've needed to pop excess CDs at some point.