Note: the section titles here are links which should take you straight back to the section. So if you find someone playing "Spot the Worldview" online, you can link them straight to this page to show them the error of their ways.
As I've mentioned before, talk of worldviews became fashionable among evangelicals when I was an undergraduate. Back then, one of the big evangelistic events the Christian Union organised was called Paradigm Shift, a term borrowed from Thomas Kuhn's book The Structure of Scientific Revolutions. As part of our evangelism training, we read Nick Pollard's book, Evangelism made slightly less difficult, which was about helping people to see the flaws in worldviews other than Christianity (Pollard writes about this approach here).
There were some good things about this approach. Engaging with the arguments of people who disagree with you is better than writing those arguments off as a smokescreen put up by evasive sinners. It's more realistic than the major alternative approach, which was (and still is) treating Two Ways to Live as inherently magical, so that the most important thing was to "proclaim" it to non-Christians as often as possible. Still, worldview talk can go wrong. Here are some ways I've seen that happen:
This is an example of the false dilemma fallacy. As gareth_rees says, theists may assume (but not show) that the worldview they're proposing does better than a major rival, and spend all their time attacking the rival. In creationists' attempts to disprove evolution, there's an implicit assumption that if evolution fails, the Christian God is the next preferred explanation. Similarly, much apologetical effort is directed against materialism or physicalism, when it is perfectly possible to be an atheist and believe in ghosts, say. Matt McCormick's useful article, Know Your Godless Heathen Positions, makes clear the distinctions between a number of possible positions (atheism, materialism, naturalism, and so on).
This is not a fallacy if an atheist is, say, a committed materialist who won't accept religion for that reason. In that case, a theist would need to clear the ground by arguing against materialism. The fallacy occurs when, having cleared the ground, the theist fails to build their own argument.
We all have views about how the world is, but many theists assume that all atheists bought a well-known brand that's available in bulk (as Christianity itself is, albeit in a variety of sizes, colours and flavours). A while back, on this thread, many theists seemed to assume that all atheists would be strict materialists. That's not how I'd describe myself: I'd say I'm a provisional materialist, at best.
Sometimes, theists assume they can argue against these atheist brands merely by mentioning their names and saying that everybody knows brand X is inferior. For example, you might be in the middle of talking about Dawkins's books when a theist tells you that "Richard Dawkins is a logical positivist, and positivism has been debunked". This doesn't work on it's own: first they have to show that Dawkins is a logical positivist (he's not, he's a scientific realist), then they have to give some argument against positivism, and lastly show it's relevant to an argument about whether his books are any good.
Evangelical Christians like to argue (wrongly) that "everyone worships something". This translates into worldview talk as statements like "everything is a faith position: I have faith in God, you have faith in human reason/science/the Conservative Party". You might hear the theist make a statement like "atheism is a religion". What could they mean by this?
They might mean that everyone has to start by assuming some stuff (that they're not in the Matrix, say, or that scientists aren't just making their results up), assuming stuff you can't show is "faith", therefore everyone has "faith", and therefore Christian faith is as justified as any other. This goes wrong in a couple of ways: firstly, it assumes that all such assumptions are equally reasonable. They aren't: for example, they can be differentiated by how easily we could tell if they were wrong. Edited: Chris Hallquist puts it better than I did, when he says that "belief in the Christian God isn’t very much at all like most of the common-sense beliefs commonly cited as threatened by Descartes & Hume-style skepticism (like belief in the reliability of our senses), but is an awful lot like beliefs most Christians wouldn’t accept without evidence–namely, the beliefs of other religions. That kind of response is very hard to reject without special pleading on behalf of Christianity, and doesn’t involve commitment to any potentially troublesome epistemic principles."
Secondly, this use of "faith" isn't how many Christians like to use the word. According to Christians, faith means putting your trust in a person. Christianity transplants notions of loyalty to friends onto loyalty to worldviews. With the exception of those of us who worship at the Church of Dawkins, atheism isn't about loyalty to or trust in a person, nor is steadfastness in a particular atheist view seen as a virtue (quite the reverse, as far as I'm concerned).
They might mean that there are atheists who, for example, organise into groups to further their aims, or raise funds for the cause. As Poke argues, even atheists may feel they should not organise into groups because "that's what religion does". The atheists should recognise that doing the opposite of what mistaken people do doesn't make you correct. The theists should recognise that forming into groups and raising money is not what makes something a religion.
Finally, they might mean that atheists imitate the worst features of religion. This could be true: both religious and non-religious groups may fall into uncritical supercriticality, the idea that it's wrong to criticise any argument that supports your position. It would be right for a theist to criticise an atheist group which fell into this trap, but not all of them do so.