On CC, there are two types: Sleep and Bind. Both of them restrict monsters from doing certain things, and are broken if the monster is hit with any direct damage.

Sleep comes from CNJ (Repose) and THM (Sleep). THM additionally gets a trait to make Sleep hit everything in a 5-yalm radius. Sadly, many things resist sleep.

Bind comes from many sources. ARC has Shadowbind, which binds a single target. CNJ has Fluid Aura, which knocks a monster back and binds it, albeit for a mere 6 seconds. THM gets Blizzard II, which binds everything around the THM, but only for 4 seconds. Finally, SMN gets Tri-Disaster, which is a ranged AoE Bind. Bind works on most things, but it only restricts movement. As such, it will not help if the monster has a ranged attack, or if it's right next to the tank anyway.

On a side note, CC is only broken by DIRECT damage. Damage over time from debuffs like Aero will not wake/unbind them. Do take note, however, that most DoTs inflict some direct damage when applied, so for the most case it only helps with debuffs placed BEFORE the CC is applied. The exceptions are Bio, Bio II, Bane, Flaming Arrow, and Shadow Flare. All of these apply their debuff with no direct damage, and as such should not wake/unbind mobs.