This science isn’t objective yet, but a list of the reptiles/amphibians/fish that seem to be unusually intelligent would be nice.

With the fish, the sharks and rays have the largest brain/body ratios – the manta ray has the largest of them all. In fact the manta ray seems to recognize something "special" about the human – somehow it allows humans to "ride" on it (and in fact it tries to "communicate" an "openness" to being ridden on). I’ve never heard of that sort of behavior outside of a few mammal species.

As for the reptiles, the crocodilians have a small cerebral cortex. But it seems that the komodo dragons and monitors have more novel behavior.

I don’t know of any amphibians with intelligent behavior – the amphibians don’t seem as morphologically diverse as the fish or reptiles are.

Birds: corvids. The *only* reason why parrots are admired for their intelligence is probably because the ONLY in-depth study of bird intelligence with a single bird subject came with Alex and Irene Pepperberg. Crows definitely have more novel behavior than parrots. Although it’s hard to predict if an Alex-like experiment would work on a crow or not.

Mammals (excluding humans): Some species of dolphin. Orcas have low brain-body ratios but this may be less relevant for very large animals (just as it means little for shrews which have higher ratios than humans do). Orcas seem to be more cultured than bottlenose dolphins even though bottlenose dolphins have been more extensively studied. The dolphin institute clearly shows research where dolphins outperformed chimpanzees (dolphins are much faster learners than chimpanzees although it is still kind of difficult to assess their cognitive capabilities). At least the dolphin institute produces published research (unlike Koko the gorilla)