At least 10 people aboard United Flight 935 were hurt when the aircraft encountered severe turbulence.  Is the airline responsible for compensating its injured passengers?

Because Flight 935 was an international flight, a treaty known as the Montreal Convention governs the passengers’ claims.  The Montreal Convention makes the airline liable for any injuries suffered on board the aircraft due to an "accident."  The definition of "accident" includes an encounter with severe turbulence.  The passenger need not prove that the airline was at fault for the accident.  Under the Convention, the airline is automatically liable.

Some courts have ruled that while an airline is automatically liable for any "accident" on an international flight, its obligation to compensate an injured passenger may be reduced if the passenger himself contributed to his injury.  One issue that typically arises in turbulence cases is whether the injured passenger should have been wearing his seat belt.  In this case, it appears the seat belt sign was off and the turbulence competely unexpected, so that should not be an issue.

As discussed here, the Convention entitles the passengers to be compensated for the emotional distress they have suffered, but only if they also suffered some sort of physical injury as well.

Finally, as discussed here, the passengers are entitled to sue the airline for compensation in the United States, and in particular in California (Los Angeles or San Francisco), regardless of their citizenship or final destination.