|MadSci Network: Neuroscience|
The very best way to think about this is to imagine all of the sensors we use nowadays in school science and in cars and houses. They are usually movement detectors or light detectors, but they can also detect many chemicals. Even the humble smoke alarm is an example.
The next thought to have is what happens if we join all of these together into one big bundle, with perhaps a screen to see which one is detecting or which are functioning /non-functioning? We have a simple computer to collect the wires but very little decision-making beyond switching off detectors and switching them on. Simple house controllers are now being sold to be the very simple "brains" that turn your lights on and off and draw your curtains when the Sun's brightness alerts a light detector. At this stage, we should revert to the Animal Kingdom.
Your jellyfish, along with all known Coelenterates, have two nerve nets of "wires" which simply inform muscles to contract when the animal is upside down, just like our inner ears. They would tell the animal where the surface is by either gravity or light detection. The evolutionary stage beyond such simple organisation is just being reached in modern houses. Nerve centres in some animal groups control area of their bodies, like the segments of an earthworm. Now earthworms actually have two large nerve centres or brains which help (1) the gut to maintain its digestive sequence and (2) the senses from the skin to coordinate the animals external musculature and movement. We all know the next step after the earthworm. It's a single nerve centre or brain which has evolved in many different groups, most successfully in the vertebrate fish, from which our large central nervous system developed.
Cephalopods (like the octopus) and flatworms (the first bilaterally- symmetrical animals, we believe) are the examples or animals with a collection of neurons we can call a front-end brain. You can check on their appearance here: Nervous Systems.
In the cephalopod’s case, it is obvious that the brain is useful to mobile hunters. Some of the flatworms have become so immobile and sedentary that it is unlikely that the nervous system suits their lifestyle.
Following your argument, it's possible for an animal to live without a brain if it is parasitic, and is therefore relying on its host for all of its needs. The distant relatives of the flatworms, the cestodes or tapeworms fit the bill. Already, they've lost their gut, so it's likely that the nerve cells are nil or very nearly so. Perhaps the head or scolex has some detecting ability, but it's more likely that the larval form or onchospere is very "neurotic" with lots of nerve cells and some coordination, in order to penetrate the gut wall when it hatches. In zoology, you must always remember that the larval form does not have to follow the adult patterns. The adult has to fit in with what the larval form does!
The list of animals without brains would be none at all, if you follow the above argument. Even those so retro as to lose their brains in evolution have a stage in their life when they have a brain. So every animal has a nervous system or a brain. It's now down to you to work out how the algae and fungi, which are not animals, manage without any nerve cells at all. They swim, move along logs and generally get around very efficiently without help, excepting when it comes to insect pollination. THEY are your list of organisms without brains.
Try the links in the MadSci Library for more information on Neuroscience.