What consequences did the destruction of the Worldstone bring?

At the end of Diablo 2

Tyrael destroys the Worldstone to prevent its corruption.

Has there been any official word about the consequences of that action? Or the lives of the people of Sanctuary has not been affected by it?

The first inhabitants of Sanctuary were super-humans called the Nephalem. They were the children of an Angel (Inarius) and a Demon (Lilith). The Nephalem were so powerful that their existence sparked the Sin War between the angels and demons. Other subplots aside, Inarius became jealous of the power of the Nephalem and created the Worldstone to contain their power.

Inarius used the worldstone to prevent the Nephalem from developing their powers, reducing each succeeding generation's power until they became normal humans of Sanctuary.

Given that, with the Worldstone destroyed - humankind may grow to significant power again and spark a new Sin War.

As you can see in the Nephalem article on the wiki, the Nephalem play a role in the quests of Diablo III. It is hard to predict the full effects with the game not yet released, but based on the lore the destruction of the Worldstone should at least make humankind significantly more powerful.