There are regions in the brain that are primary concerned with sensory input; e.g. parietal for sound, occipital for vision. The hippocampus is thought to be involved with short term memory, while many regions of the cortex are thought to be involved in long-term memory.

I believe most of memory and other higher thought is stored in the cortex, but I'm sure there is memory storage in other parts of the brain, since there are animals that lack cortices and maybe some that lack brains altogether yet can still remember things.