Low gravity (relative to earth) seems to give people no problems once they get used to it. We've had people in weightless environments for months. However the human body can easily adapt to those conditions, and gets rid of what it perceives as excess muscle, bone mass, and fluid volume. Which is fine, unless the person wishes to return to a higher gravity world-- like Earth. Astronauts use rigorous exercise programs to stay in shape enough to return to Earth, though the longer they stay in space at zero G, the longer it takes to return to full health on Earth.
Of course, any planet that retains and atmosphere will have much more gravity than is experienced in a space station or shuttle. The difficulty of adjustment would naturally decrease as the differences in gravity decrease. You might only feel jet-lagged for a while moving between a 0.9G planet and Earth.
Unfortunately we don't know as much about how the human body could adapt to higher gravity environments--the nearest is Jupiter, and even if we could get there, surviving the pressure is far beyond our current tech. But we can get some idea observing the reactions of people in centrifuges and fighter jets. At the equivalent of 9 Gs well-trained pilots black out in seconds. It's exhausting just sitting for an hour at 3 Gs. It's been estimated that people could get along at up to 2 Gs (if with a reduced life-span due to the strain on the heart). But beyond 1.25 to 1.5 Gs normal activity would feel burdensome. Short, lean but muscular people with strong heats would tend to cope best. See Habitable Planets for Man, a free PDF.
Of course, if your inhabitants aren't human, you don't need to worry, though many of the issues with high gravity would apply to any humanoid, if not quite to the same degree. A human-tall biped would need an absurdly large and powerful heart to pump blood up to his brain in a 9G world. And tripping would be life-threatening.