As the article notes, those of us with pets already had strong suspicions that this was the case. However, after a friend's hamster screamed in the night apparently due to a bad dream, she googled to find out and found a brief article on the subject which she shared. I googled a bit more and came up with this more serious article about the same study.

Animals have complex dreams

Actually, having seen the legs of a sleeping leopard moving in his sleep (in the wild, to show how habituated to the safari vehicles they are), I can say that I find it cool to know that when non-human animals appear to be dreaming, they probably are. My cat may be having the same dreams as my friend's hamster, though for him, they are probably good dreams.

Thanks Jan for the find.

My cats display REM during sleep, proof they are dreaming.   Like Hop's cat, sometimes they'll wake up and howl.