This is a brief overview regarding the relation of Christianity and the occult in published RPGs. There are a number of sources which have suggested a systematic connection between playing RPGs and real-world occult activities. You can find references to these as well as responding articles in my links section below.
The short answer is that there are a few RPGs with occult material, but most doe not. There are hundreds of RPGs which have been published around the world, covering an enormous variety of genres and settings. Many of these have no possible relation to the occult, such as the many espionage and science-fiction RPGs which have no fantasy or magical elements. However, there are definitely a few which do have real-world information. Notably there is the French game "Nephilim" published by Multisim in 1991 (and later adapted into English). There the player portray fictional spirits which are behind various real-world occult conspiracies that are described in the game.
However, the majority of RPGs have no such information -- including the market leader Dungeons & Dragons (D&D). When magic appears, it is commonly what I would term "scientific" style rules, where abstract power points are spent by the player to achieve an effect. There is no description of the words or gestures used, and no discussion of possible philosophies behind them. I discuss this tendency at more length in my essay, "Breaking Out of Scientific Magic Systems". While the concept of casting magic spells does appear in the game, it is a thin device -- parallel to similar references in popular movies such as "Lord of the Rings".
Now, that some people may find this thin device itself objectionable. If you as a parent object to the appearance or imagery of casting spells, then obviously D&D and similar fantasy games are a concern for you -- along with a host of movies, television shows, books, and other sources. I discuss this issue more in question 2. My point is simply that D&D does not have secret information that makes it in principle different from a fantasy-themed movie or television show.
My advice to parents is simple: read the game. Unfortunately, the tabletop RPG industry does not have a voluntary rating system like movies or video games in the U.S. However, there are also no hidden secret messages, and you can view the entire material simply by flipping through the book (unlike a video game or movie). You don't need to learn it in detail, but you can usually get an idea of what is portrayed without undue effort. If a book portrays real-world religions, magic, or adult themes, it nearly always has a clear disclaimer indicating such. A few game companies seem to deliberately court such controversy in order to gain publicity.
There have been claims made that real-world occult societies intersect and recruit from role-playing communities. That is, even if there is no actual occult content in the published RPG books themselves, members of the RPG community tend to be involved in the occult moreso than other hobbies. This claim cannot be a priori dismissed, but it is hard to either prove or disprove.
I can cite a number of studies which show no evidence of such a link. There have been a large number of psychological studies concerning the relation of role-playing with other psychological and social tendencies. None of them showed any correlation to criminal or occult behavior. Furthermore, in 1995 the Cultic Studies Journal published a study of 217 subjects comparing frequent gamers with satanic dabblers and found no psychological relation.
As with published game texts, RPG players are tremendously varied. There are gamers of many different backgrounds, races, and religions. There are certainly gamers who are neopagans and atheists. There are also many gamers who are Christians, as represented by organizations such as the Christian Gamers Guild. I survey the demographics of role-players on my "Who are Roleplayers?" page.
In short, no.
I have a webpage which lists dozens of peer-reviewed psychological studies of role-playing gamers, primarily in the U.S. None of these have shown any correlation between RPG play and violent or suicidal tendencies.
Of course, there have been RPG players who have committed suicide or murder. Given that tabletop RPGs have printed millions of copies over thirty years, it is expected that some people who play RPGs will also commit suicide or other violent crimes. A few cases have been publicized, such as The Disappearance of James Dallas Egbert III. However, no study has found that role-players are any different than the general population in this respect. None of the studies that I have seen (referenced in the article mentioned) have found any statistical or causal connection.
I do not know of any churches which have officially taken any particular stand regarding role-playing games. However, there are role-playing games developed by Church groups as aids in Christian education. These include The Way, developed by the youth works section of the Västerås Bishopric of the Church of Sweden and endorsed of Bishop Ytterberg. This is a series of three RPGs intended as tools for use in youth confirmation courses, presenting moral issues for children to ponder. There is also Dragonraid, developed by Adventures for Christ as part of the Lamb's Bride Project.
At the same time, there are RPGs which are undoubtably objectionable to Christianity. The French games In Nomine Satanis and Magna Veritas (adapted into English as the game In Nomine) are both to some extent parodies of Christian religious views. White Wolf's "Demon: The Fallen" game appears to have deliberately courted controversy by having players portray demons as misunderstood protagonists.
I think it is important to look at particular games rather than generalizing. Both "The Way" and "D&D" are role-playing games, but they have vastly different approaches. As with any serious hobby, I think a parent should look carefully at the RPGs which a child plays.
There are a few volunteer organizations which are specifically devoted to either criticizing or defending role-playing games. If you are interested in more general information on role-playing, I would recommend also looking at role-playing game companies and gamer groups. The focussed organizations include:
This is a small set of links to other sites on the web related to the religious implications of RPGs.