In the Epic of Gilgamesh what made the gods change their mind about destroying mankind?

Answer 1

Well there's a few different versions of this. In the ones I am aware of, the gods didn't really agree on this issue. Enlil was all for flooding the world, but Enki thought that was wrong, and warned Utnapistim (or Ziusudra, depending on the version you read) behind Enlil's back. Enki was always a good friend to mankind- but not all the other gods were.

Have some links on sumerian mythology.
http://www-etcsl.orient.ox.ac.uk/
that's the oxford direct translations. They're pretty good, although I know a few scholars who disagree on some points- ie these guys really try to edit out all the sex.

http://www.sacred-texts.com/ane/sum/index.htm
And this is Kramer's work- he's very well respected, even if his stuff is a little out of date. He explains things very clearly.

Answer 2

Even the "gods" were terrified of the great flood. It was apparantly a threat even to them. When Gilgamesh offered his sacrifice, after coming out of the ark, the "gods" crowded around the smoke coming from the sacrifice, as refugees crowd around a campfire. They (supposedly) recognized their need for the sacrifices their creation could give them, and relented of the disaster they had planned.