A newborn's skin is prone to rashes of all sorts, but luckily most of these rashes are harmless and go away on their own.
Salmon patches (called a "stork bite" at the back of the neck or an "angel's kiss" between the eyes) are simple nests of blood vessels (probably caused by maternal hormones) that fade on their own after a few weeks or months. Occasionally stork bites never go away.
After the first few days or weeks (or even months), new rashes can appear. Read more about newborn's skin and rashes.
Slideshow: Slideshow: A Visual Guide to Birthmarks