I am able to break blocks in Creative mode, but when in Adventure mode, it's just a single punch. Not breaking. At all. Now I've tried Survival, the block broke. In Aventure mode, I used a pick-axe and it broke this time! It was for fist. This will be hard without commands enabled.
This isn't a bug. In the adventure mode, you can only break blocks with the spezial tool. For example you can only break wood with an axe or stone with a pickaxe. Other tools or just your hand can't destroy blocks.