The smallest living organism that has a brain is believed to be the Bryozoan, specifically the Bugula neritina. These tiny marine creatures measure just a few millimeters in size and possess a simple nervous system that can be referred to as a brain-like structure.
On the other hand, the biggest living organism that does not have a brain is the Honey Fungus (Armillaria ostoyae), which is a type of fungus. The largest known living organism on Earth can cover an area of over 2,385 acres, primarily found in the Malheur National Forest in Oregon, USA. This organism spreads through mycelial networks that connect and can decompose wood and other organic matter, but it lacks a centralized nervous system or brain.