Yes, I think so. Here is some of the evidence that is important to me.
Scientific evidence is just beginning to be gathered. But we do know two things: First, puzzle work develops specific areas of the brain (according to the type of puzzle). They become more active, and apparently grow more neural connections, and possibly more neurons. Just like muscles, parts of the brain grow with exercise. Second, there is some evidence in the scientific literature that those who stay mentally active experience a slower decay of brain function if they later develop Alzheimer's. Solid evidence of this will take years to collect. But in the meantime, we can use what seems likely to be true.
Scott Flansburg is a unique genius when it comes to math problems. He's even been tested on Stan Lee's Superhumans. He set himself out to become fast at math, developed game-like methods, and can do many things people would think are impossible. And he uses a different part of his brain for doing math than most of us - this has been seen on a brain scan. (You can also learn his program; it's cool.)
My mother did crosswords and word-finds for years. Her Alzheimer's proceeded slower than most, and this (among other factors) reduced suffering a lot for her and our family. One distinct benefit was that, even after she had lost the ability to do puzzles, she could sit and work at the book and think she was doing them, and that made her happy.
Note: It's not all about puzzles. My wife's father did advanced theology and also prayed and read his bible. He's surviving a serious brain injury very well for over 3 years now. He enjoyed theological reading until recently, and still enjoys Bible reading and prayer.
For myself, I wrote two hubs this month. One was about a game: Pangrams, and I worked it intensely. This activated my creative intelligence, allowing me to complete another hub about the history of the Battle of Britain, which included some very challenging creative thinking based on a lot of research.
So, yes, I encourage puzzling, challenging reading, writing, and thinking. As my friend, life and athletic coach Dan Millman says: "Use it or lose it."