If I am using the correct form while doing a standard deadlift what primary and secondary muscles are being targeted?
There's a classic quote about the power clean, attributed here to Charles Staley, that applies to your question:
"You know when you run down the field, catch the ball and then hit a defender? It works that muscle."
The deadlift works all the muscles. However, it's not quite the same as the running-jumping-hitting-the-defender athleticism of the clean, because it's more about being straightforwardly strong. It could be more accurate to say, "You know when you pick up the other guy, throw him to the ground, and pin him there? That muscle." The deadlift is about picking things up, or maintaining structure and posture against external forces.
The target muscles of the deadlift are all of them. The secondary muscles of the deadlift are all the rest.
Lower Back and Posterior Chain
That said, though the deadlift involves the grip, arms, shoulders, upper back, lower back, abs, neck, and legs, it particularly makes strong the lower back and the posterior chain. The excellent resource exrx.net puts the deadlift as primarily using both the erector spinae (isometrically) and the gluteus maximus. Second to those muscles in exrx's run-down are the quadriceps, hamstrings, calves, adductor magnus, and traps.
The erector spinae, abdominals, and related muscles are those that lock the trunk in place during the deadlift, keeping the spine safe.
The glutes, hamstrings, and related muscles are referred to as the posterior chain, which is critically important in nearly all sports. These are the muscles that drive hip extension, such as is involved in most basic athletic movements like running, punching, and jumping.
Training the deadlift makes for a solid back, a strong butt and legs, and as a bonus, pretty much everything else gets stronger too. It stands to reason: barring partial-range-of-motion exercises, the barbell deadlift is usually the heaviest lift one can perform. Performed correctly--which is to say, with very heavy weights--the entire body usually ends up supporting more weight than with any other lift.
Which Muscles, Exactly
The book Strength Training Anatomy by Frederic Devalier details all the muscles used in the deadlift, in graphical form. Those muscles labelled in bold or shaded in red are used.
A larger, more complete version can be found here.
The deadlift works more muscles than any other lift, but what sets it apart from other lifts is the attention it gives to the back:
The deadlift builds back strength better than any other exercise, bar none. (From Starting Strength, 3rd Edition)
Specifically, the deadlift works the legs (hamstrings, quads), hips (glutes, and supporting muscles), abs, forearms (for grip strength), and back (almost everything... spinal erectors, lats, rhomboids, levator scapulae, trapezius).
Where you will tend to "feel" the lift if you are using correct form is in the hamstrings and lower back. In the set-up, pre-pull position, you will feel a stretch in your hamstrings as your hips are high and your spinal erectors are pulling your back into rigid extension. Your back fights your hamstrings for control of your hips, and your back must win. That means your hamstrings will feel stretched and your back will be in isometric contraction.