Do the villains know Batman has no superpowers?

The answer would depend on which villain, and which universe you're speaking about.

We are told that Bruce Wayne chose the image of a bat to "strike fear into the heart of his enemies". In fact, everything about his physical appearance is used to create a false image that he is more than just a man. Particularly in the movie incarnations, his body armour makes him look more muscular than he actually is, and he uses his gadgets and the fact his armour gives him some bullet-proofing to make people think he can fly and is immortal, but this is just as evident in the comic universes. None of this would "strike fear" into anyone if they all knew he was just a guy in a suit, so all of this suggests that most of his "enemies" are supposed to believe that he has supernatural powers.

Batman's primary purpose was to fight crime on the streets of Gotham. The image he created is primarily aimed at the "street" criminals - thieves, murderers, muggers etc. Super-villains are a different case, and many of these have (in various universes) discovered his identity, including Bane, Deathstroke, Despero, the Riddler, Hush, Man-Bat, Max Lord, Ra's Al Ghul, Owlman, Killer Moth, Lex Luthor, and Joe Chill.

A good example of this contrast between how "regular" and "super" criminals view Batman is found in the 1989 movie, in which the regular criminal 'Eddie' talks about "the Bat" killing his friend 'Johnny Gobs' and sucking all the blood out of his body, showing that he believes the supernatural stories; whereas The Joker describes Batman as "a man dressed as a bat" with a collection of "wonderful toys". Again, this contrast is seen in comics too.

Of course, knowing his identity isn't necessarily the same as knowing he doesn't have any powers; but some of these stories have involved villains knowing his identity due to telepathy (Despero, for one), so arguably they would know both.

To the common street criminal, Batman must appear to be supernatural. This is all based on his premise:

Criminals are a superstitious cowardly lot. So my disguise must be able to strike terror into their hearts. I must be a creature of the night, black, terrible... - DC # 33 (1939)

Also confirmed in Batman: The Musical.

Nobody among the common criminals knows who the Batman is, or if he is human or meta-human or even if he is just one guy. He nearly always emerges from the darkness, his form is hard to detect due to his quickness, his cape, his skill at using shadows to his advantage. - reddit

Maybe his rogues are just as tricked.

Joker: He sure gets around for one guy.
Two Face: Well that's where you are wrong. I don't think it is one guy. The way I figure it, Gordon has a bunch of them stashed some place, like a SWAT team. He wants you to think it is one guy.
Croc: Well you know what I think?
Joker: Not the robot theory again!
Croc: Well it could be.

A few, like Ras Al Ghul and Bane, know his real identity and know that he is man, albeit with superior detective skills and an indomitable spirit.

One radically contrary theory is that Batman wants villains - and everyone else including us - to think he has no superpowers, while his strength, agility, endurance, and ability to recover from injury all suggest otherwise.

This is a very brief summary of the excellent and hilarious video Batman's Secret Super Power. In short, Bruce Wayne first becomes a master scientist (depicted studying test tubes of mysterious liquids) before being able to train his body to perform blatantly superhuman feats of strength -- and, as we see in later comics, superhuman agility, reflexes, ability to recover from injury, etc.

Batman will never reveal this secret. Being underestimated is one of his greatest weapons. The comics go to great lengths to never reveal the truth in words -- and even frequently say that Batman has no superpowers. But focusing not on what we're told, but what we're shown, it's easy to read between the panels. Batman whipped up some secret sauce ala Captain America or Bane. And fair play to him. There is no USADA in crime fighting.

The video concludes that his ultimate superpower is the character's massive popularity, which "lets him get away with pretty much everything". I think a big part of that popularity stems from him not having superpowers.

On top of all the other answers, Batman sometimes gets involved in situations which make him seem superpowered to everyone's surprise. Not always on his own volition though.

In season 3, episode 2 of Superman: the Animated Series, Batman is missing. Superman decides to don Batman's costume and fight crime in Gotham. Bane takes the beating of his life, with the Mad Hatter and Riddler as witnesses. That must have become quite the story among Gotham's criminals.