Type of damage that can kill mobs:

ContactDamage caused by contact with a Cactus.
Entity attackDamage caused when an entity attacks another entity.
ProjectileDamage caused when attacked by a projectile.
SuffocationDamage caused by being put in a block.
FallDamage caused when an entity falls a distance greater than 3 blocks. Feather fall can reduce this number.
FireDamage caused by direct exposure to fire.
Fire tickDamage (over time) caused due to burns caused by fire.
MeltingDamage caused due to a snowman melting.
LavaDamage caused by direct exposure to lava.
DrowningDamage caused by running out of air while in water.
Block explosionDamage caused by being in the area when a block explodes.
Entity explosionDamage caused by being in the area when an entity, such as a Creeper, explodes.
VoidDamage caused by falling into the void.
LightningDamage caused by being struck by lightning.
SuicideDamage caused by committing suicide using the command "/kill".
StarvationDamage caused by starving due to having an empty hunger bar.
PoisonDamage caused due to an ongoing poison effect.
MagicDamage caused by being hit by a damage potion or spell.
CustomCustom damage (from a plugin).

Data adapted from the Bukkit JavaDoc.