It seems to be commonly accepted in discussions on this site (viz. the first two answers to this question) that there is the magical world and there is the muggle world and there are strict boundaries between the two; that anything that muggles know about is completely non-magical. But this doesn't hold up to events as depicted in the books: wizards commonly traverse through and interact with the muggle world (The Ministry of Magic is in London – think about all the routine interactions that implies on a daily basis for all the people who walk in through the public lavatories). Wizards are born to muggle parents. The Night Bus drives on Muggle roads. It's always the case that the magical world is right under the noses of the muggles, but the muggles are just bewitched into not noticing the magical things, or rather, the magical side of things, all around them.
With that in mind, we have plenty of evidence that animals in Harry Potter are not the same mundane species as we know them. Similar to Are Owls in Harry Potter universe normal ones?, are all snakes in the Harry Potter universe magical creatures or normal animals?
Consider Parseltongue, a complete language that only snakes, magical creatures resembling snakes (the Basilisk) and wizards can speak. Furthermore, the ability to speak Parseltongue is strictly inherited or imparted with dark magic – no one can learn to speak it. Dumbledore learned to understand it, but could not speak it, and Harry lost the ability to speak and understand it when Voldemort’s piece of soul inside him was killed.1
Here in the real world, there is tons of ongoing research into understanding animal communication as it relates to human language (and even understanding human language itself). The smartest, most communicative animals discovered have impressive skills, but that's still orders of magnitude away from every snake being able to hold a conversation (even a simple one like Harry has in the zoo).
Without devolving into arguments on the semantics of unknown phenomena vs. magic, what is the explanation for snakes being able to talk? The fact that muggles in the Harry Potter universe haven't discovered how to talk to snakes is circumstantial evidence that it's not just hyper-intelligence.
The distinction hinges, I think, on why Parseltongue is magic-based. The simplest explanation that makes sense to me is that snakes are part magical2. The next simplest is that Parselmouths share ancestry with snakes.
1: J.K. Rowling Live Chat, Bloomsbury.com, July 30, 2007: http://www.accio-quote.org/articles/2007/0730-bloomsbury-chat.html
2: I suppose the simplest explanation is actually that J.K. Rowling wrote it that way for purposes of the plot and didn't consider all the ramifications of the existence of magic on reality as science currently understands it. (Consider Harry Potter and the Methods of Rationality.) But still! I'd like to know why Parseltongue is magic-based instead of a pure linguistics challenge.