You can find a full list here.
Arcane Enchanted - Nightmare - Monsters summon a purple laser beam that slowly spins and deals arcane damage. With multiple of these going, you're going to be navigating a maze to get through it.
Avenger - Hell - Only champions can have this. Whenever you kill one, the others hit harder. The last one left will hit the hardest of all.
Desecrator - Normal - Enemies create a fiery zone of damage underneat player characters that deals damage over time.
Electrified - Normal - Enemies spew out lightning in all directions whenever they take damage.
Extra Health - Nightmare - Self-explanatory. The bonus health is significant.
Fast - Nightmare - Self-explanatory. The monsters are considerably faster.
Fire Chains - Nightmare - This appears on champions only. When close enough together, there are chains of fire linking the champions to each other that deal damage over time to players who stand in the way.
Frozen - Normal - Enemies will spawn frozen orbs that spin for a while, growing in size, and then explode. The explosion deals cold damage and freezes you in place for a few seconds.
Health Link - Hell - When attacking a champion with this trait, the other champions nearby will take part of the damage. This makes it tough to take down groups, but has no affect if one is isolated.
Horde - Nightmare - This can only appear on elite (yellow) enemies. They get extra minions.
Illusionist - Normal - Enemies can create 4 clones of themselves. The clones have severely lowered damage and health.
Invulnerable Minions - Hell - Only elite (yellow) monsters can have this. All the minions are invulnerable until you kill the main monster, and then they all die immediately when the main one dies.
Jailer - Normal - The monsters can imprison players so they can't move for a few seconds.
Knockback - Normal - The monsters can knock back the hero a significant distance (a little over one screen length). The player is slowed significantly after the knockback effect for a few seconds.
Missile Dampening - Inferno (Maybe?) - I haven't personally seen this one yet, so it is either Inferno only or doesn't actually exist. If the source is to be believed, it seems that this will work similar to the Wizard's Slow Time ability.
Molten - Normal - Enemies leave a trail of fire where they walk that deals damage over time to players who stand on it. They also explode a few seconds after they die, dealing damage in an area around their corpse.
Mortar - Normal - Enemies gain a ranged attack that fires a volley of a few lobbing bombs every couple seconds. This is very dangerous for ranged characters.
Nightmarish - Normal - Enemies that hit you will cause you to flee for a few seconds.
Plagued - Normal - Enemies can create giant pools of poison that deal damage over time to players. These pools are quite large and last a long time and can easily cover the entire floorspace of a room.
Reflects Damage - Nightmare - Dealing damage to the enemies deals a bit back to yourself. The effects of this don't seem to be very significant from my experience.
Shielding - Normal - Enemies can turn invulnerable for a few seconds at a time. The effect is fairly frequent, with about a 50% uptime of invulnerability.
Teleporter - Normal - Enemies can teleport.
Vampiric - Nightmare - Enemies gain life when they deal damage.
Vortex - Normal - Enemies can suck you next to them from more than a screen length away.
Waller - Normal - Enemies can create walls to prevent escape. They are very good at placing the walls, and will often barricade you in with them. Many ranged abilities cannot go over the walls, even things that appear like they should. For example, a Witch Doctor's Firebomb cannot go over the wall.