As a kid, millions of new neurons are still forming - it's only as an adult that there's less "neurogenesis" (new neurons being formed). Less, rather than none. On the whole I'd guess that an adult brain is made of the same neurons/molecules today that it will be in a decade. The neurotransmitters and all the blood & fluids would be newly generated though.
Beyond that I have no idea if any part of your body is completely static. Are adult, uninjured bones always made of the same molecules or is there constant regeneration there as there more obviously is with hair?