Azmodan is one of the two remaining Lesser Evil and a notable figure in Diablo 3. Given that the Prime Evils and 2 out of 4 Lesser Evils have been killed, technically Azmodan and Belial (the other remaining Lesser Evil) are the remaining rulers of Hell.

This guy has never been seen prior to Diablo 3, but was a notable figure in the Diablo lore as being one of the two Lesser Demons to have started that war that banished the Prime Evils from Hell.
In Diablo 3 Azmodan seems to have a very prominent role, appearing in at least one cinematic and in-game. It has also been revealed that this guy will be the act boss of Act Three. Azmodan, being the incarnate of the seven sins, also controls demons that represent a single sin. Three of these have been revealed to be in the release of Diablo 3, being Ghom (Gluttony) Cydaea (Lust, previously known as the Mistress of Pain), and Rakanoth (Unkown what he represents so far, possibly wrath) . It is unclear if the other demons will be added in patches or in expansions.
It has been revealed that Azmodan is invading Sanctuary to get the Black Soulstone, a powerful Horadrim artifact that is now in Lea's possession that he can use to increase his power and rule over Hell as a Prime Evil. Here is the cinematic where he can be seen talking about this plan:
As you can see from the cinematic Azmodan is huge! He is fat, has insect like legs not unsimilar to Duriel, and is decorated in treasures. Blizzzard seems to have done a good job making him represent all of seven sins, as each can be seen in distinct features on his body.
In the beta, when you kill one of those treasure goblins, it adds a lore entry that makes a reference to the goblin's master, a demon known as the lord of greed. This might be one of Azmodan's servants.

Some cool trivia about Azmodan:
- Looks like the Pit Lord from World of Warcraft or Warcraft 3.
- His name might be seven letters long to represent each of the 7 deadly sins.
- Is a reference to a demon in Hebrew lore known as Asmodai.