Can channeled spells (Disintegrate, Firebats) crit? What about targeted AoE spells (Blizzard) or "wandering AoE" (Energy Twister)? Is there a good clean way to identify what can and can't critically hit?
Yes, Yes, and Yes. I don't think there's anything that can't crit actually.
Abilities which do damage over time, either as a DoT, or Channel, have a chance to crit on each individual tick as near as I can tell. I don't believe there are any abilities in game which do a fixed amount of damage and are incapable of a critical strike.
According to the answers on "How does crit affect beam spells and DOTs?", both of those types can crit.
My guess is that Blizzard made everything able to crit after learning from WoW that if you have spells that don't crit, it throws off itemization: you have some classes/specs that do not want crit at all, and some who find the crit stat overpowered. Since Blizzard has been trying to make the game more accessible and make items desirable for all classes (see Wizards wielding 2h axes), I suspect this is why they made everything able to crit.
Is there a reason you want to know what does not crit?