http://blog.paleohacks.com/grow-new-brain-cells/

The article says research has shown growth into adulthood in the hippocampus and the sub ventrical zone. Other areas of the brain are yet to be determined if there is growth or not.

Things you can do:

1. Exercise
2. Curcumin supplement
3. Eat blueberries
4. Caloric Restriction and Intermitent fasting
5. Omega 3s
6. Low sugar diet
7. Green tea and\or EGCG supplement

"Though an exciting prospect, neurogenesis is subject to the rest of the diet, human bodily processes, and other activities and stresses going on in your brain. As researchers have also noted, too much neurogenesis could be just as bad as too little."

"It is also important to note that many new neurons borne via the process of neurogenesis die within 2 weeks."