Sponges (phylum Porifera) are sessile multicellular organisms that live predominantly in seas and oceans. They don’t have tissues or organs, and therefore, they don’t actually have a nervous system. However, they do have bipolar and multipolar cells that resemble nerve cells, which are found in the middle, “jelly-like”, layer.
Sequencing of some sponge species showed the presence of many genes associated with neural cells, such as genes that code enzymes for neurotransmitter synthesis and synaptic transmission. It is important to note that these genes have other functions in the organism. It has also been observed that some sponge larvae can respond to outer stimuli and show various “taxis” behaviour – phototaxis (response to light), geotaxis (response to gravity), rheotaxis (response to water current). Phototaxis has been closely studied in species Amphimedon queenslandica (class Demospongiae), a sponge native to Coral Sea.

Potassium channels have been observed in that same species, as well as glutamate, GABA, and NO systems, which have been investigated in Ephydatia muelleri, another species of class Demospongiae. Electrical signalling has been noted in glass sponges (class Hexactinellida). These sponges have bodies comprised of a syncitial tissue and their skeleton is made of silicon dioxide. The scientists were able to measure the action potential (5s long, with 29s refractory period) and deduce this signal relies on potassium and calcium ions.
Some scientists even suggest that sponges used to have a nervous system, but lost it during evolution – they introduced several hypothetical scenarios for this event, proposing that sponges lost their nervous system in order to focus on filtering.

Literature & more information:
^{Habdija et al: Protista-Protozoa, Metazoa-Invertebrata, Alfa, 2011, Zagreb
Evidence for Glutamate, GABA and NO in Coordinating Behaviour in the Sponge, Ephydatia Muelleri (Demospongiae, Spongillidae)
The GABAergic-like System in the Marine Demosponge Chondrilla Nucula
Where is my mind? How sponges and placozoans may have lost neural cell types
Elements of a ‘nervous system’ in sponges}