Sketchy question and no definite answer.
Everyone has their strengths and they should focus on the same. Some are good with logical thinking. These guys become mathematicians. Creative thinking is another great asset where a person can imagine myriad stuff for improving on the stale and the mundane. These guys become artists/musicians. Another is lateral thinking where a person needs to think outside the box. People good at it can become good managers as they are able to tackle situations with unprecedented methods. Of course, nothing is exclusive and people are good at some parts and not so much at others.
IF one really wants to engage his brain, i think one should invest his time in solving really interesting logical/abstract puzzles. Start with the Monty hall problem. Such a simple premise, but such an unexpected answer. I was really astounded when the answer was revealed.
I think one should engage one's untapped mental faculties for its own sake rather than as an attempt to increase brain power.