Is it possible for any animals today to have more than one brain?
To some degree the answer depends on your definition of what counts as a brain.  

Bilaterally symmetrical organisms tend to have some level of cephalization, which involves the concentration of sensory and inter-neurons at one end of the organism (the head).  

This aggregation of neurons at the head is typically more complex than aggregations of neurons elsewhere in the body and so it gets designated as a brain whereas the others are designated as ganglia (if they are outside the central nervous system or nuclei if they are within the central nervous system).  

In vertebrates, cephalization is very well developed so the brain is typically much more complex than the ganglia (although the enteric nervous system is pretty awesome, its not the brain). However in many invertebrates, the ganglia at the head of the organism (its brain) is not much more complex than the other ganglia around the body.

For this reason, many invertebrates can survive decapitation (at least for a while) and some like the flat worm, can famously survive and regenerate their head after decapitation.