When I was levelling my demon hunter I was able to use vault to quickly get away from an area where damage was happening or smoke screen to break freezes and jailer cages.
I've had some difficulty with arcane, jailer, frozen as they can really stack up quickly.
I do use ignore pain to great effect, but that doesn't help against everything.
What can I do on a barbarian to counter the various elite affixes? Which will break freezes and jailers?
Wrath of the Berserker is your go to skill in times of emergency. While in that mode, you are immune to control effects (I believe this is the only barbarian skill that breaks control effects). However, don't pop it as soon as a fight starts, you'll want to save it for emergencies due to its long cool down.
For more less pressing situations, leap is a great way to escape being trapped. Its pretty fast recharge, and if you time it right, you can be mid air while the frozen triggers and it'll miss completely.
Typically, your best bet is to maneuver carefully and just be constantly on the move and avoid those effects completely. Sometimes this is very hard to do if the enemy has jail and vortex, in those situations you'll have to stagger your leap and ignore pain to survive the long stretches (or pop WToB).
Use the passive Juggernaut skill.
