NASA has run experiments that suggest that humans could probably survive and adapt to planets with 2.0g. Which actually covers quite a lot of planets; a planet twice the size of earth, with a similar density, despite having a mass 8x higher than Earth, would only have a surface gravity of 2.0g, from what I have read on the subject (I got curious and started looking it up). Twice the size of earth gives us a lot of room for planets of different sizes, and that doesn't even account for lower-density planets, which do exist.
It wouldn't surprise me if 2.0g would cause longterm medical problems (heart having to work harder, etc), but it's probably safe to say that the medical requirements to handle that would be within reach.
NASA also stated that at around 4.0g, human physiology begins to fail. Basically your body isn't equipped to either pump the blood to your brain or to handle the pressure required to do so.
In a funny way, lower gravity may just be harder on humans.