All it does is change the sound of your voice for a bit by changing your vocal chords(due to how it is less dense than air).
You would need to take several lungfulls of helium to be even close to death. Which would be, as explained before, due to a lack of oxygen in the blood.
But that does not mean that you really do, per se. It can potentially be dangerous. Inhaling helium from a balloon will not kill you, but you could get dizzy or pass out and fall down. Which isn't really horrible, but not fun.
And, to state the obvious, don't...you know...take a hit of helium straight from one of those big canisters at the grocery store or where have you. Those tend to cause bursting of lungs because of the pressure which they shoot the helium. And burst lungs tend to cause well, death and lots of internal bleeding.