None to speak of, as long as you don't breathe too much of it. If you breathe enough to become unconscious (less than you might think, with Helium) there could be brain damage or even death. In that case, you would have killed several billion brain cells. Huffing Helium to get dizzy or pass out is about as dangerous as any other suffocation game.
You should know that Helium, because of its physical properties, displaces oxygen in the blood very rapidly. Getting high on it is extremely dangerous...not because of brain damage (except when you die) but because there is great danger of suffocation. Once the blood is saturated with He, it does not always de-saturate quickly. It may not be possible for sufficient oxygen to reach your brain quickly enough to prevent death or serious brain damage. It may also not be possible to reactivate your breathing reflex.
Divers and others who work with Helium are taught these things. Just because it is used in cute little balloons and makes you talk funny, don't underestimate it. It can be deadly.
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