Back sleepers usually prefer medium- to low-density pillows (typically labeled as “medium” and “soft”) because they provide the appropriate level of neck support.
Belly sleepers are usually more comfortable with low-density pillows — they allow you to easily turn your head to one side to breathe.
Side sleepers often prefer a medium- to full-density (“firm”) pillow, depending on the distance from the head to the mattress (a person with broader shoulders, for example, would require a more supportive, thicker pillow). A contour pillow (with a recess for the head and support for the neck) may be a good choice if you sleep on your back and/or side.
