Why are some neurones unmyelinated?
In this answer I'm building off of @Fizz's pointer to the nice paper by Laurence Knowles, "The Evolution of Myelin: Theories and Application to Human Disease" [1].

First -- I just want to point out that your question is adaptationist, which means that it assumes that myelin is on some axons and not on others for a reason. Whereas maybe evolution just hasn't gotten around to it yet, even though myelinating all axons would actually be beneficial. 

That said, here are two of the main downsides of myelination: 


It might cost energy. This one is a bit controversial, but at least one study has found [2] that while myelin decreases the energetic cost of firing an individual action potential, the whole apparatus involved in myelin (e.g., in the CNS, the oligodendrocyte, its processes, and the sheath itself) actually costs more energy than it would cost to just open all of those ion channels without saltatory conduction. 
Myelin and its associated oligodendrocytes/Schwann cells take up space. This is likely to be especially important in areas of the nervous system where there are a lot of neurons packed into a small area. 


So from the adaptationist perspective, the question is whether the benefits of myelinating an axon, such as increased conduction velocity, increased conduction fidelity, axon protection, and supplying the axon with nutrients, are worth the downsides of taking up space and possibly increasing net energy use. 


http://www.ashdin.com/journals/JEM/235996 
http://www.jneurosci.org/content/32/1/356