Intoxicating or stupefying.
The cocktail was a heady mixture of spirits.
Tending to upset the mind or senses.
We looked out from a heady outcrop of rock.
Exhilarating.
The rock concert was a heady mixture of their greatest hits.
Intellectual.
Kierkegaard is rather heady reading for a high school student.
Rash or impetuous.
He made too heady promises, and when it came time, he was never able to fulfill them.