If you are looking straight down at a solid block in survival mode, and you start to punch the block, the breaking animation will not be shown.

To test: stand above a block, make sure you are only on that block and not any others (place blocks around you to make it easier). Look straight down (any angle above looking straight down doesn't work) and hold left click. Depending on the block's breaking time, it may take longer. But the block should soon break, without any animation of the breaking occurring, aside from particles.