Which animal has the smallest brain in relation to size?

The smallest primate brain is detained by the mouse lemur (Microcebus murinus) of Madagascar: 0.004 pounds (2 g) (this is also the smallest primate in the world).

Amongst vertebrates, the smallest brain in relation with the body size seems to have belonged to a dinosaur: Stegosaurus was 6 m (20 ft) long and weighed 2 tons. Its brain was just the size of a walnut! To compensate this, the spine presented a second "brain" in the pelvic area.

http://news.softpedia.com/news/Top-10-Brains-83944.shtml

The sponge has no brain at all, and thus certainly fits the bill...

Coral reefs are living and have no brain.

http://www.princeton.edu/main/news/archive/S16/62/14C41/index.xml?section=newsreleases