Not at all. It only looks that way. The black color of the water in the Black sea comes from decomposition of vegetable matter. This is caused by bacteria that live in the water. The Black Sea also happens to be rough, gloomy and often covered with a thick fog, which is why it was originally called Pontus Axenus (Inhospitable Sea) by the ancient Greeks.
The Red Sea got its name from the reddish algae that thrive in its waters.
As for the rest of the worlds’ seas, they seem blue for the same reason the sky seems blue. Light from the sun is broken up by the water particles. Since the blue wavelengths are the shortest, they get broken up and bounced around more, making them the dominant color.