Wikipedia has a short but fascinating page listing animals by the number of neurons they have. There’s only about a dozen entries on there, but most interesting is that there is an animal with no nerve cells at all.
It’s called Trichoplax and apparently is a “a simple balloon-like marine animal with a body cavity filled with pressurized fluid”.
Apparently humans don’t come top of the pile, as both elephants and whales have more neurons.
However, it’s not the best referenced article in the world, to say the least, so I’m taking this last claim with a pinch of salt for the time being.
If you know better, do update the article with some more reliable sources.
Link to ‘List of animals by number of neurons’.