Minecraft wiki entry for Overworld, associated text: The maximum number of blocks that can be generated in the Overworld is approximately 921.6 quadrillion (9.216×1017) blocks, assuming a distance of 30,000,000 blocks in either direction.
The total area is about 8 times the surface of the Earth, or approximately the surface area of the planet Neptune.
This means that storing a filled world, with no entities or block entities, would require 3.6864 quintillion (3.6864×1018) bits (409 petabytes) for the block data alone, based on the fact that each standard block is assigned 4 bits of information.
By manually modifying the game, it is possible to generate the world up to 2,147,483,647 blocks (the 32-bit integer limit) in either direction.
A 1:1 (1 block = 1 meter) scale map of the Earth, built-in Minecraft, would be 510.9 trillion (5.109×1014) blocks in size.
Assuming the map is one block deep and uses 1 byte per block, its size would be approximately 475,800 GB (464.7 TB).
A Moon-sized map would be made of 37.95 trillion (3.795×1013) blocks. Its data size would be 35,340 GB (34.52 TB).