fanzine = fan + magazine
A fanzine is an independent magazine devoted to a specific cultural phenomenon. Fanzines are unofficial, mostly non-professional, and generally created by fans for fans. The Internet and print media being what they are, though, fanzines are inching their way toward the mainstream.
I was surprised to learn (from Wikipedia) that the word fanzine was coined way back in 1940 by Russ Chauvenet, who also coined the portmanteau word prozine, professional + magazine, as the opposite of a fanzine. The first fanzines were devoted to science fiction, Amazing Stories being perhaps one of the most well-known of those early fanzines today. Many of the 20th century's greatest writers got their professional and creative starts by either writer for or reading Amazing Stories.
The ability of the Internet to bring together fans from across the globe has moved fanzine-dom largely online, so that now there is even TheFanzine.com, which began in 2007 as a nonprofit, but is on the move toward selling advertising, blurring still the line between professional and non-professional.