We're born on Earth. We die on Earth. Our entire species has evolved without ever needing to factor in the possibility of leaving this planet; in fact, the first person to blast off into space only did so just over 50 years ago. So it's not surprising that any amount of time in zero-g has an effect on human physiology.
Just a few of the effects include spaceflight osteopenia, which is where bones lose density of about one percent per day; muscular atrophy, since it is much more difficult to get exercise; radiation exposure, thanks to the lack of a protective ozone layer; and a slowed cardiovascular system, since our heart was designed to pump blood through a body weighed down by gravity.
In fact, astronauts returning from a sojourn in space -- such as serving aboard the ISS -- take a long time to recover. Chris Hadfield, for example, was estimated to take up to a year to recover from five months aboard the ISS.
Another fun thing that can happen is that fluids redistribute around the body, leading to a puffy face, balance problems and intercranial pressure. This last can also have an effect on vision, as fluids in the brain apply pressure to the optic nerve -- the video below explains in detail.
Will humans ever adapt to a zero-g lifestyle? Well, maybe. We'd have to have many generations being born, living and dying up there before we would see any change at all, though. Probably the better option for long-term space travel would be the deployment of artificial gravity.