Though science fiction has always shown humanity's future was jetting among the stars, NASA wanted to make sure there weren't any side effects before they started sending people on long journeys. Sadly a recent study shows that there is some possible danger of an increased risk of Alzheimer's disease. The culprit is iron HZE particles, which increased the accumulation of protein "plaques" in the brain. Even worse news for future Astronauts, there is no known shielding for iron HZE particles.
On Big Think they explain that the study used mice being modeled for an Alzheimer's study, and found that the exposure to iron HZE particles increased the onset of the biological and chemical signifiers of the disease. This is by no means definitive, but it does place another obstacle in any plan NASA may have for mission beyond the Earth and the Moon.
It seems that the research is still in its early stages, and it may come out that this is not as a big of a concern as it seems at first blush. It also isn't clear from this report how this exposure would measure up to real world timeframes. The paper was published in the journal PLOS ONE.