Recently the Discovery Networks produced a fictional movie in the form of a documentary called Mermaids: The Body Found. While the movie was indeed a work of fiction, many people thought it was real, and it attempted to present that mermaids could theoretically be real.
The reality is that mermaids are not real. If they were indeed real, we would have known about them by now, despite the fact that they would be close to intelligent as us, if not as intelligent as us.
Mermaids would most likely be sea mammals, and despite the fact sea mammals can often stay under water for long periods of time, they would still need air to breath, and thus must come up to the surface occasionally.
Mermaids would also require a viable breeding population in order to keep the species going. Even endangered animals are occasionally seen in the wild. This includes sea creatures who would have a easier time staying hidden. Sea mammals especially, because as I said before hand, sea mammals must come up air, making it harder to hide from us if they intended to do that. The amount of ships on the oceans, and even the great deal of the population that lives along coast, would make it even harder for an sea mammal to remain hidden.
Another reason why mermaids most likely do not exist is because no bodies have ever been found beached.
Sea mammals occasional swim up onto beaches and usually die for various reasons. This has been going on for as long as we can remember, and most likely even longer then that. Despite this there has never been one recorded instance of a mermaid ever beaching itself.
Also, considering how common it is to have a camera, the ability of the government to keep mermaids a secret if one or two were to ever beach themselves would be very difficult. This ability would go down year after year as more and more buy mobile devices that have inbuilt cameras that can upload photos to the internet.
Another thing to consider is that they would most likely eat fish, same as we do. They would probably even hunt for fish in the same areas as we do. It's highly unlikely that such creatures could exist into the 21st century and never been caught in a fisherman's net.
Dolphins, which are suppose to be the smartest creatures in the oceans, are caught in fisherman's nets all the time, so even a mermaid should at least occasional get caught. With the increase of commercial fishing throughout the past few decades the odds of a mermaid never being caught decrease year after year.
While there have been many alleged "sightings" of mermaids they have been few and far between, and are most likely the result of mis-identification, mass hysteria, or an outright hoax. In fact most alleged mermaid sightings occurred before the 20th century. People back then usually misidentified things if they didn't know what they were looking at, same as they do today. People also tended to embellish things back then, same as they do today.
The fact remains is that such a species, no matter how intelligent they are they are, can not remain hidden for this long of a time.
And one more thing: Our oceans have a lot trash in it. Won't an intelligent species like a mermaid have tried to do something to get us to stop polluting their homes with our garbage?