The risk of dementia will be getting larger and larger as you age, and 2/3 of all dementia cases are Alzheimer cases.
If you want to stay in the best shape that your brain can be, you need to stay in shape. Exercising will keep your nerve cells from worsening. Taking walks, to light jogging is all what you should be aiming for. This is something that you should do from the moment that you're self conscious, but some people don't like exercise.
Your memory starts worsening at the age of 30.
While on the topic of memory, did you know that the more synaptic plasticity there is, the better detail in the memory will be put? This happens in stressful situations where the body releases glukokortikoids (stress hormone), and adrenaline.