A small dose of aspirin taken daily reduced cancer overall (25%), and the researchers report the results for several different types of cancers (at different levels of prevention) but also all-causes of death (10%). BBC has a short but nice write up. There are side effects and complications of taking daily doses of aspirin so this must be taken into consideration.
But this study published in the Lancet was a large study with over 25,000 subjects. Additionally, this was a randomized study and not just a natural study of finding people that did and did not take aspirin and look at the outcome.
And regarding the brain the paper also reports a reduction in brain cancer.