Above: a reptilian alien. When he's not busy leading the Masons
This sounds like lots of other people with fixed beliefs; the content of the belief is secondary. The few things that separate these beliefs from garden-variety delusions is that these people often claim these beliefs in groups, much like religion - it's one thing to come up with Nibiru or a man riding a horse into the sky on your own when no one else believes it, but it's different when there are a bunch of people on conspiracy websites or at your mosque reinforcing each other. (Not any more likely to be true mind you!) The other thing is the degree to which these people endorse their beliefs. A few people during the Campingocalpyse last year actually did attempt to kill children or pets and quit their jobs and give away their money. Most of the rest of the "believers" found excuses to act in ways that clearly did not accord with their stated beliefs. This is why it's sometimes useful to make "bets" about beliefs, because a) it makes the believer define a concrete outcome and b) it forces an immediate consequence. Frequently people become less certain or just end conversations when such an option appears.
That said, it's time to find people who claim they believe this and try to get them to endorse their delusion - take a loan out that they have to pay back 5,000% interest the day after the apocalypse, will their house to you, SOMETHING. If they won't, they now have to contort (again) about why they're acting exactly like someone that doesn't really believe what they're saying. And if they will - hey! Free money! There's a price for irrationality.
The Harold Camping apocalpyse parties last May were awesome. Are we going to have 2012 parties or what? Let's get planning!