It seems like it would make more sense to have your most powerful servants leading your armies, rather than some orc who only cares about revenge. Is there a plot explanation or a description in film canon that explains why Sauron made this choice?
I'm going to point out firstly that, although Azog isn't a character in the book, I think this is a valid question in both book and movie canon. In the book, the Orc legions are commanded by Azog's son Bolg, who appears in Desolation of Smaug as the leader of the orcs who track the dwarves to Lake-Town. I'm going to try to be canon-neutral for the most part.
To my knowledge there's no canon explanation of why Sauron doesn't put one of the Nine in command of his forces at this point. We know that they're active around this time, at least in the books, because they capture Minas Ithil (Minas Morgul) in TA 2000, about 1000 years before the events of The Hobbit.
The most plausible reason for wanting an Orc in charge is that Sauron is laying low, and doesn't want to reveal himself. Anybody who cares (i.e. The White Council) know that the Wraiths only answer to Sauron, so having them openly leading armies of Orcs would give him away instantly1. It's easy for someone like Saruman to rationalize a marauding orc pack (Which is what Sauron is counting on), but it's harder to explain an orc pack being led by an unquestionable servant of the Dark Lord.
Going into movie canon now2.
As to why one of the Nine isn't in charge, one possible interpretation of Radagast's encounter at Dol Guldur (The fight with the Wraith-shade) is that the Nine are still dormant at this point, and haven't yet acquired the form they'll have in the LotR movies. This may contradict the bit of canon trivia I pulled out two paragraphs ago, or it might indicate that eight of the Nine are active in Mordor, and the Witch-King is only just waking up.
This is semi-confirmed and semi-refuted by The Battle of the Five Armies, where all Nine Nazgûl appear in Dol Guldur to defend Sauron against the White Council. Although the Nine to appear (seemingly refuting my theory), two things suggest to me that they're not yet at full strength:
- They only appear in shade form. This is far from conclusive evidence, since everyone involved in that battle has some connection to the Spirit World, but it's interesting.
- They're much less substantial in combat. Compare this battle to, for instance, Aragorn's confrontation on Weathertop in Fellowship of the Ring. Elrond is slicing through Wraith-shades like a hot knife through butter, banishing them temporarily only for them to re-form moments later. With Aragorn, they're more sluggish about it; although he can't definitively defeat them until he starts using fire, his blades do seem to repel them for a certain period of time (longer than the Wraiths in BofFA)
As to why Azog, specifically, was in charge: based on The Battle of the Five Armies, it seems as though Sauron was counting on Azog's irrational desire to exterminate Thorin. In the movie, Gandalf says (paraphrased because I obviously can't verify the exact wording yet) of Sauron's plan:
Gandalf: Sauron wants to take the Mountain. Not just for its gold, but for its location; its strategic position. This mountain is the gateway to the Kingdom of Angmar, in the north.
So it would seem that Sauron has a very good militaristic reason for wanting the mountain, a goal which requires Thorin and company to be dead. Azog wants Thorin dead. It's a match made in Mordor3.
1 In fact, this is exactly how Gandalf puts the pieces together in Desolation of Smaug when he learns that the Witch-King's tomb has been broken open from the inside4:
Gandalf: The Nine only answer to one master. We have been blind, Radagast, and in our blindness the Enemy has returned.
2 There needs to be a better name for this. I'm going to start calling it the Jacksonverse, which is such an obvious name I'm surprised I haven't heard it more often
3 Yes, I know: technically it's a match made in Dol Guldur. "Mordor" rhymed. Yeesh.
4 I'm going to ignore the fact that Gandalf already figured this out from the Morgul knife Radagast gave him in An Unexpected Journey, since Jackson apparently did
So far as movie canon is concerned here is what we currently know:
- At some time in the past the Nazgul were buried.
- Gandalf visits their tombs and finds them empty.
We don't yet know when the Nazgul got out.
We don't know where they currently are.
We don't know if they've got to recover their strength in a similar manner to Sauron.
As I implied in a related question, this is an ongoing series that is due to finish shortly with the third movie, and we are not being given all information up-front. Based on the information in my answer to that question, it does appear as though the Nazgul are going to play some kind of role in the third movie, and an answer may be forthcoming then. We'll find out.
Despite that, we can make some surmises, as follows.
First of all, it's clear that the wise don't yet know that Sauron has arisen again. As Saruman states the first movie:
What enemy? Gandalf, the enemy is defeated. Sauron is vanquished. He can never regain his full strength.
It's also clear that Gandalf's discovery that the Necromancer is actually Sauron is, so far as movie canon is concerned, the first intimation of such.
Now, one conceivable reason for that is that Sauron does not (for unknown reasons of his own) wish to declare himself yet.
And it should be obvious that if he had sent the Nazgul out (assuming that he has access to them at this point in time in movie canon) he would have declared himself.
So therefore he holds them back and sends a lesser captain.
However, that's all speculation - evidence-based, but still speculation. We'll really have to wait for the third movie to discover what they're currently up to.
It might also have to do with the fact that Azog is actually a fairly competent general, as shown in the third Hobbit movie. His army has the advantage of surprise, a high-ground position and a fairly advenced signalling system, enough forces to spare and reinforcements at the ready.
In my point of view as we see from the others answers it was clear that Sauron doesn't want to reveal himself. So he didn't send the Nazgul to lead the army. He choose Azog because Azog knows the terrain well and the army only follows his orders and seeing that he wants to defeat the Dwarves once and for all he choose Azog. Sauron attacked Erebor because he realized that after capturing it he will weaken the alliance of Men, Elves and Dwarves by defeating the Dwarves once for all so that they didn't help at the war of the ring and it will be easy to the elves and men without Dwarves. If Azog captures Erebor the road will be open for him to enter Angmar then at the instruction of Sauron help Saruman to defeat Rohan and then join Mordor to defeat Gondor once for all. If Azog joins Sauron first Rohan will get defeated and Gondor allies get finished and Gondor gets defeated easily. After finishing Men, Sauron will defeat the remainder of alliance of Elves easily and Sauron will rule whole of Middle-earth