This article is about a guy who discovers and shares very odd Internet broadcasters that you'll probably never come across any other way. He outlines a few of them:

"There’s a station in Washington state that streams live audio from a microphone that’s 23 feet underwater...Then there’s the internet station that has outdoor weather instruments connected to an analog synthesizer, so when you tune in you hear the current weather conditions expressed as a continuously changing frequency."

"In the U.K., there’s an internet station that plays nothing but radio station jingles. But I think my favorite...is Payphone Radio Network. The New Yorker who started it calls in and records his thoughts about whatever happens to be on his mind at the time and then plays the recordings over his internet station. The kicker is, he calls in exclusively from public payphones!"

Another one is from Canada:

"This month I’ve been listening a lot to a Canadian internet station I discovered called “Easy Listening Christmas,” playing artists like Percy Faith, Hollyridge Strings, Manheim Steamroller, Ray Conniff Singers, etc. It’s old-school holiday music for sure but it won’t put you in a coma for Christmas."

Delving into Quirky, Compelling Corners of the Internet Radio Universe