Who else produces Duplo-sized blocks? I gather that Mega Bloks Mini Bloks are the same size as Duplo, and are compatible with it. Do any of the other major brick manufacturers make similar bricks?

Knowing the possibilities can help when sorting out collections of bricks purchased second hand.
There are several Chinese companies making DUPLO clones, many are listed in this fascinating article by Anthony Tomkins of UK LUG The Brickish Association. 

Communist LEGO, a review of some Chinese copies