To answer this question, let’s think about how our brains grow to the size they normally are. During development, our brains are built in a complex ballet of neuronal birth, migration, maturation, and even death. For mammals, this process starts in the womb and extends through adolescence. Scientists interested in the process of brain development have known for a while that brains make too many neurons, with too many connections between them, during certain stages of development. Eventually, these excess neurons die, in a process called apoptosis (definition: programmed cell death). A brain could end up overgrown with neurons if either too many cells are born, or too few die.
What is the consequence of a brain with too many neurons? There is no clear answer. Some scientists think that overgrown brains are a marker of certain forms of autism. There are many, many scientific studies that have compared the brain size (or, more often, the head circumference) of children with autism spectrum disorders (ASD). In some cases (but not all), ASD patients have brains that are larger than those of normal children. The proposed theory is that for some small percentage of ASD individuals, the waves of neuronal growth and programmed death that occur during the first few years of childhood, are disrupted. When this happens, certain parts of the brain end up with more neurons.
Now, it’s very important to say that this result is fairly controversial. Scientists at the National Institutes of Health recently questioned the methods of some of the scientific studies reporting early brain overgrowth in ASD patients. For these studies, larger brains were measured as an increase in head circumference, as compared to national averages. The problem: the national averages used were biased towards small head sizes. So the studies significantly overestimated the difference in head size between ASD patients and neurotypical babies. When compared to updated national averages, the differences decreased. Also, differences in head size are not permanent. By adulthood, any head size differences between ASD patients and normal individuals has vanished.
Lastly, keep in mind that even if there are differences in the number of neurons in the brains of autistic patients (for example, in their frontal lobes), it’s not clear to what extent these changes will contribute to the features of the disorder. Changes in head/brain size are not observed for all ASD patients, so the changes are probably not required. They may, however, be symptomatic of larger problems with brain development that are causal in ASD.
Some other quick notes:
A while ago, we received a similar question, asking if having a bigger brain made you smarter. Here’s a link to the answer (which is, maybe).
And finally, the flip side of your question: what would happen if a brain has too few neurons? A graduate student at Stanford is studying fruit flies that have radically smaller brains and bodies, because they were hatched in conditions were food was an extremely limited resource. Interestingly, although these flies appear to have massively fewer neurons in their brains, they seem to act just like normal flies. The PhD student will be spending the next few years trying to figure out how their brains are built, and work, with fewer numbers of neurons.