According to Wikipedia a zine is:
An abbreviation of the word magazine—is most commonly a small circulation, non-commercial publication of original or appropriated texts and images.
Zines are written in a variety of formats, from computer-printed text to comics to handwritten text (the most famous example perhaps being Aaron Cometbus’s eponymous work). Topics covered are broad, including political, personal, social, or sexual content far enough outside of the mainstream to be prohibitive of inclusion in more traditional media. The time and materials necessary to create a zine are seldom matched by the sale of zines. Zines are seldom copyrighted and there is a strong belief among many zine creators that the material within should be freely distributed. In recent years a number of photocopied zines have risen to professional status and have found wide bookstore distribution.
The exact origins of the name “zine” and the moment when the word was first used are controversial. The history of “zines” is clearly connected with that of Fanzines, which began in the science fiction subculture in the 1930s, and particularly with the fanzines that emerged as part of the punk rock movement in the late 1970s. “Zines” enjoyed a brief period of attention from conventional media in the 1990s, when a number of “zines” were collected and published in book form. Some believe that the widespread adoption of web browsers starting in 1996 marked the end of the classic period for print zines.
“Zines” continue to be popular. Currently “zines” are important to the Do-It-Yourself (DIY) movement. Recently galvanizing social issues such as globalization, environmentalism, media conglomeration, American imperialism and consumerism have been addressed by “zinesters.”
An ezine:
is a periodic publication distributed by email or posted on a website.
Ezines are typically tightly focused on a subject area. Ezines in concept are reworking of the popular magazine format of monthly, or weekly topical publications, in an electronic format.
A webzine:
is an ezine hosted on the World Wide Web rather than in print. Unlike blogs, which are published ad hoc, a webzine tends to be published on a regulated basis (weekly, biweekly, monthly). Webzines also maintain an editorial control system whereas blogs do not. Another distinguishing characteristic is that webzines bypass the strict adherence to the reverse-chronological format; the front page is mostly clickable headlines and is laid out either manually on a periodic basis, or automatically based on the story type. Some people also use the term to refer to any magazine published on the Web.
There are also underground ezines and diskmags but I know I haven’t created one of those.