Pure hydrogen gas contains no oxygen so asphyxia is a possibility (causing dizziness possibly leading to unconsciousness and ultimately death due to insufficient oxygen reaching the brain). Hydrogen forms explosive mixtures with air or oxygen, so the possibility of ignition makes inhaling hydrogen very hazardous (would you want your lungs to look like an exploding hydrogen balloon?). Industrial hydrogen may be contaminated with other gases depending on its source and some of these could be harmful (carbon monoxide for example).
A mixture of hydrogen and oxygen called hydreliox is used in very deep diving (500-700m) to avoid nitrogen narcosis (the dissolution of nitrogen in blood due to high pressure). Some mixtures also contain helium. I believe the mixture must be handled with extreme care since it is explosive.