"Здоровый смех" -- sincere loud laughter; laughter without reservation.
There is "искренний смех", which is similar but not necessarily particularly loud.
"Бурный смех" is also similar, with a degree of uncontrollability.
"Неистовый смех" has a manic quality to it. When it's too manic then it's just that -- "маниакальный смех".


Groups of male teenagers have a knack of producing this particular kind of overenthusiastic "здоровый смех" that is sometimes referred to as "гогот".