We do not really know what the interstellar medium looks like up close and personal. If it is just stray hydrogen atoms and a few microscopic dust grains ( micron-sized is common) then at their expected densities you are probably in for a rough ride once you pass 50 percent the speed of light. The dust grains become lethal, interstellar 'BB shots' pummeling your spacecraft like rain. At the higher velocities needed for interstellar travel, 90 percent the speed of light, these dust grains may be infrequent but each punctures your spacecraft, and leaves a very impressive hole many times their own diameter across like small bombs.
But the situation could well be worse than this if the interstellar medium contains lots of ice globules from ancient comets and other things we cannot begin to detect in interstellar space. These impacts even at 0.1c would be fatal...we just don't know what the 'size spectrum' of matter is between interstellar 'micron-sized' dust grains, and small stars, in interstellar space. My gut feeling is that interstellar space is rather filthy, and this would make interstellar, relativistic travel, not only technically difficult but impossible to boot! This is an issue that no one in the science fiction world has even bothered to explore! The only possible exception is in Star Trek where the Enterprise is equipped with a forward-directed 'Brussard Deflector' (that big gold dish just below the main saucer) which is supposed to sweep away particles before they arrive at the ship. This is very dubious technology because hydrogen atoms are not the main problems a ship like that would have to worry about, especially traveling inside a planetary system at sub-light speeds.
