What happened when Hercules died?

If you are going by traditional, actual Greek mythology, the answer is complex. His wife was tricked by a jealous centaur into putting the centaur's blood on Hercules' cloak. This poisoned and nearly killed Hercules. But then Zeus (Hercules' father) took pity on his son and turned Hercules into a god (rather than a demigod, like Hercules was before).