For a starship moving at 0.3 c, a typical grain of carbonaceous dust about a tenth of a micron in diameter should have a relative kinetic energy of 37,500,000 GeV. Our hypothetical star mission with human crew moving at a substantial fraction of light speed will run into about thirteen of these dust particles every second over every square meter of frontal area.
This gets interesting when put in the context of cosmic rays. Most galactic cosmic rays, which as Andrews notes are completely ionized atoms accelerated to extremely high energy states, have energies between 100 MeV and 10 GeV. You can see the overlap. Travel fast enough and even small grains of dust behave like energetic cosmic rays as our vessel encounters them.
Physical protection and magnetic protection are examined.
Check out the Carnival of Space week 90 for a lot more.