How is it that some nebulae are rotating and others are not? First, I should make it clear that this isn't a question about angular momentum (unless I may have completely missed something). It is my understanding that a nebula must have some inherent initial spin before collapse to form a solar system (and if it doesn't have that spin, only a star is produced). Then, basically, Conservation of Angular Momentum takes hold (and this is where the rotation is more noticeable), thus producing the accretion disc around the star, then planetary bodies, etc.
Now, what determines the initial rotation of a nebula before collapse? Why is it that some nebulae do not have an initial rotation before they collapse?
 A: While there is always Some element of spin (it would be very difficult to have an absolutely non-rotating body, or cluster of bodies) if it is very low, we can treat it as effectively zero, as there are various drag effects as the nebula coalesces.
The reason most objects (whether they are nebula or not) do end up rotating is from the very effect you note - as you move in towards the centre, rotation effects increase due to the Conservation of Angular Momentum, and these outweigh drag effects in a lot of cases.
A: As @Rory said, there will always be some spin, but it can vary from very little to very much.
The primary source of spin in nebulae (also for galaxies), is torque from the local environment.  Nearby nebulae, clouds, stars, etc can exert a net torque on the nebula (or galaxy) giving it angular momentum.  This is the primary source of spin for nebulae.
After inflation, there were random over-densities of angular momentum in different regions---just like there were over-densities of mass, etc.  This effect is primarily important for larger objects (e.g. galaxy clusters), and I don't think it has any roll on nebulae... but I'm not positive.
A: I am sure you have since figured this out, since it’s been several years since you asked, but I had this question earlier, and more research answered my question, so I figured for others who may have a similar question, I’ll answer with what I found. 
So apparently, some of Earth’s oldest meteorites contain xenon-129, which is a gas, even at relatively low temperatures, and it binds to nothing since it’s noble. This means that it wouldn’t have condensed and mixed with the rock during accretion, and therefore we must conclude that it is a by-product of radioactive decay. The parent isotope is iodine-129 which has a relatively short half-life relative to the age of our solar system (17 million years). Furthermore, it’s a very heavy isotope, so it’s likely from a supernova explosion. Since there was a short time between the explosion and the formation of the solar system, it is believed that such an explosion sent shockwaves through our nebula, therefore triggering the rotation. From there, gravity took over to condense the nebula, and the rest is just the Nebular Theory. 
In general, it appears to me that things tend to trigger the events, but it may very well be in part due to thermal fluctuations, though the average temperature of the universe is about 3K, which is barely above absolute zero, and therefore might be negligible because of its low density, though I wouldn’t quote me on that. 
Source: The Cosmic Perspective, Bennett, et al.
