How much time passed between Diablo II and Diablo III?

20 years

You learn that in many of the lore and books you pick up

I can't remember the exact books, but for example I heard about Andariel deciding to side with Diablo and eventually getting defeated by some brave warriors 20 years ago in one of the books I picked up in Act II

And as far as I know, no major events happen to the world in the meantime other than the ones that that directly relate to the story

Tyreal says:

20 years passed between the destruction of the Worldstone (depicted in the final cinematic in Diablo II) and Diablo III. Tyreal's actions obliterated Mount Arreat and much of the surrounding area, including himself.

It took nearly that much time for Tyreal to reform himself, and when returning to Heaven he was put on trial.

As a result he left heaven, falling as a "star" and beginning Diablo III