A significant branch of current research (worked on primarily by people in statistics and computer science) is in an area called data mining. Doing a quick search, this set of tutorial slides came up near the top.
Basically, data mining is the study of VERY large databases of information (such as credit card activity for a particular CC company) in an attempt to find statistical relations that might otherwise be hidden in an immense amount of data. Based on your demographic and your history, they can statistically lump you into a category of what you’re expected behavior is. If you are a cab driver, then 12 purchases of gas a day might be the norm, whereas that would be a huge red flag for most of us. Things like sudden overseas purchases and multiple anonymous transactions are obvious things to look at. The harder problem is to tie together a couple of gas purchases with some online gambling, a plane ticket purchase and an electronics purchase. None of those things individually might be enough to trigger a problem, but taken together, if they are outside your normal behavior pattern, could signal trouble.
This is the same sort of statistical theory that is applied by some grocery stores. If you have a card to swipe at checkout to get sale prices, they have a record of what you bought. Statistically, they might know (just as a toy example) that if you are buying a particular brand of diapers and baby formula but NOT graham crackers or shampoo, then your demographic statistically prefers a certain brand of coffee. If you are not currently buying that coffee, they may print out a coupon with your receipt in an attempt to get you to try it. More controversially, data mining techniques have turned up correlations between things like your credit history and your auto insurance claims. AFAIK, some auto insurance companies are now using credit checks to help determine what your premiums should be.
Anyway, its all the same idea. Mangetout is correct: neural nets are technique in the data mining world (but there are many others). Sorry for the detail if you didn’t want it, but it’s a very interesting field.