Which animal has the smallest brain?

"The fruit fly is the smallest brain-having model animal. Its brain is said to consist only of about 250,000 neurons, whereas it shows 'the rudiments of consciousness' in addition to its high abilities such as learning and memory."

https://ui.adsabs.harvard.edu/abs/2005PhyA..350..144S/abstract

Rotifers are very small in physical size. A single individual may be smaller than a large protozoan like an amoeba or a Paramecium. They also have very few cells. So these are probably the organisms with, literally, the smallest brains.

Of course, as the common refrain goes, size isn't everything! You have to consider what you do with what you have. Among animals, sponges have no nervous system of any kind and Cnidaria (jellyfish, Hydra, anemones, ...) have a "diffuse" neural network although there are some concentrations of cells. However they do not have a central nervous system at all, so no brain as officially defined. However, you are more generous in your definition and would include them. They generally do have more neurons than a nematode.

If you want just small pieces of a nervous system, probably the record is the cardiac ganglion of the lobster (or crab, crayfish ... any crustacean). This collection of just nine neurons sits inside the heart and is responsible for producing the heartbeat. It functions perfectly well totally isolated from the rest of the nervous system and does something -- produce rhythmic activity -- that might be deemed somewhat complex. For true complexity, look at the crustacean stomatogastric ganglion. It has fewer than 30 cells but produces a whole series of rather complexly patterned activity to control the movements of the gastric mill. Furthermore, it can change from one pattern to a completely different one under different conditions. It gets my vote for "most with the least".

https://courses.lumenlearning.com/wm-biology2/chapter/phylum-rotifera/

This question has bothered me a little because it lacks a definition of "brain." There are several.

This is the first line from Zb's link:

"I am trying to find out which organism has the smallest brain. By brain I mean neuron, cluster of neurons, or anything resembling a neuron."

Obviously that's what the excerpt she quotes is based on.

Most sources differentiate between the vertebrate and invertebrate brains:

"2. Zoology. (in many invertebrates) a part of the nervous system more or less corresponding to the brain of vertebrates."
http://dictionary.reference.com/browse/brain

(I'm assuming most readers here will have at least a dim idea of what the vertebrate brain is. :-] It's that gray jelly-like mass that doesn't function before 6:00 am unless jump-started with coffee.)

I just can't help but pass along this 4-min. video clip called "How to dissect a fruit fly brain." It doesn't live up to its name, though, ending just as the brain is finally exposed after the fruit fly is literally torn to bits with tweezers under a microscope.
http://www.poetv.com/video.php?vid=37454