Omegle, the video-chatting platform favored by bored teens and perverts that randomly paired users around the world, shut down on Wednesday night after nearly 14 years in operation, according to a farewell message posted by the site’s owner.

In the lengthy message, which centers on the importance of preserving free speech on the internet, Leif K-Brooks, the owner of Omegle, attributed the shutdown to “a constant barrage of attacks on communication services, Omegle included, based on the behavior of a malicious subset of users.”

“I’ve done my best to weather the attacks,...