Here's some abilities that seem like we'd be able to use them:

Fire/Blizzard/Thunder IV: Voidsent enemies have already used Void versions of these abilities.
Haste: Buffy buffy.
Slow Spell: Instead of skills that happen to cause Slow and Shadow Flare, the actual "Slow" spell.
Inspirit: Increase Skill/Spell speed of self. Seems like a useful thing to cross-class from something else later on.
Darkness: We can use Holy. Where's the opposite?
Hundred Fists: Monks had it in 1.0. It ought to return... eventually?
That ability enemy lancers use to AOE in the four Cardinal directions: Yes please?
Shell: Scholars just have Protect while White Mages have Proshell. Perhaps another healer will just have Shell and both it and Scholar can carry Protect and Shell at once?

Here's some abilities that I don't think we'll get:

The En- spells: There's no actual elemental wheel in the game in relation to enemies, right? Applying an element to our weapons does nothing.