1) The papyrus medium in early Christianity was available only to elites and intellectuals, which undoubtedly contributed to the Hellenization and philosophization of early Christianity.
2) The Protestant Reformation emerged largely due to the power of the printing press and the popularity of preaching ministries. Protestantism's central characteristic was that it was a religion of the Word: the written Word and the spoken Word were at the very core of magisterial Reformation theologies.
3) Televangelists influenced by the celebrity culture of Hollywood have shaped an entirely new Pentecostal theological tradition that hinges on prosperity, divine blessing, the accumulation of wealth, and personality cult.
These are obviously just a few of the more obtrusive examples; elsewhere, the influence of media is more subtle. But I think it exists, nonetheless. Consider the following observations from Ogbu Kalu:
...media technology has an innate culture...
...every transcendental idea must be mediated. So religion is intrinsically woven into various forms of media representations. Communication is essential for building community. It is at the heart of the church's existence. The church is under mandate to communicate the gospel, reveal itself to the world, and dialogue and guide through a creative use of symbols and media. Thus, each new form of media provides the church with new language...
Religious users could attempt to shape media to their needs, but media too could reshape the religions, and even trivialize the content and create a religious counterculture.
African Pentecostalism: An Introduction, 104-7
If you're aware at all of postmodern theories of language, you'll know that scholars have argued that our entire worlds are shaped by the grammar and vocabulary we use to conceptualize the world. Someone who speaks German will understand the world and the relatedness of things to each other differently simply by virtue of his/her different idiom. In this light, Kalu's remark that different media offer religions "new language" is very interesting. It does, indeed, seem that the different media we use to frame our religious conceptual worlds affect the way we think. Someone who is raised in a rock n' roll church will probably have a very different concept of "worship" than someone who is raised in a church that uses hymns. This may even have deeper implications, like for example on the way they conceptualize God. The rock n' roll God might be fun and have a sense of humor, whereas the hymn God might be quieter and more noble and austere.
Also interesting is Kalu's remark that different media have innate cultures. This is certainly true of the Internet. Think, for example, of the polarizing consequences of Internet message boards like MADB. They have created a cadre of militant apologists, as well as a cadre of equally militant exmormons. The blogosphere, meanwhile, encourages everyone to have a voice. I recently listened to a podcast on feminist Mormon blogging. The panelists argued that the blogosphere provides disenfranchised people who might never speak out-- like Mormon housewives-- the opportunity to let their voices be heard. This does, as Kalu suggests, tend toward creating something of a "religious counterculture". If you've read Thomas Friedmann's The World Is Flat, you have encountered his similar argument that the online encyclopedia Wikipedia has taken knowledge-creation out of the hands of a few educated elites and democratized it, so that anyone and everyone can be involved.
Media like General Conference tend to emphasize top-down doctrine construction, and although testimony meetings encourage some lay involvement in the life of the church, they largely reinforce the top-down polity. Journals like the FARMS Review have had some influence in reversing this trend, allowing doctrinal revisions to filter up the ranks from below. But it's still intellectuals and academics who have the agency in journals like FARMS. With the advent of the Internet, all of that changes: anyone can play a role in doctrine-construction, including many people who might otherwise never even think to undertake such a pretentious task. It is a much more democratic realm, wherein things like common sense, pop culture, interfaith dialogue, and grassroots concerns are allowed to play a much greater formative role. I don't think that Mormons on the Internet could escape being in some sense "Internet Mormons," even if they wanted to. We're rarely aware of such influences, and have difficulty mitigating them even when we are aware.
-Chris