This was once known as customer behavioral profiling, although some I/O psychologists would probably have you believe otherwise that there are far deeper sentiments that consumers attach to the everyday and ordinary that surprisingly have monetary value. The most common example of predictive modeling in the financial services is credit scoring.
In the USA, credit scoring is a basic data analysis of a person's (or business') ability to maintain good credit standings and pay off debt. The higher the rating, the lower risk the person is to taking on more debt, or so the working practices go. Such factors like how many lines of credit a person has, what the revolving balances are, how much is paid off at the end of each billing cycle, are there any missed or late payments, current balance on your primary savings account, etc. Oddly enough, you actually have to take on more debt and faithfully pay it off to raise your credit score. The top major credit bureaus that amass credit data on individuals are Equifax (ScorePower), Experian (PLUS score), and TransUnion. If you are responding to an online ad about getting your free credit report, it's very likely that it's a consumer program managed by one of these companies.
So who uses this scoring methodology? Banks, of course, so they can lend you money for a home loan or extend credit to you for a HELOC; Utility companies (Gas, Electric, and Water services often require $25 deposits for customers who have poor credit); Apartment managers; Cable service providers; Private and public companies who look at a job applicants' credit history.. the list goes on.
Consumers are kind of screwed to begin with since each "hit" on their credit report influences their scoring as well. There isn't enough transparency with how scores are calculated to see if the report was accessed for financial reasons (buying a new house or car, applying for a platinum credit card) or for living reasons (relocation to a new city, getting gas service hooked up to a new apartment). And, there are hardly any resources for consumers to realistically "fight the system" when bad credit history is slapped onto their virtual account. I digress.
Predictive modeling helps companies identify their prime target for new or existing products and services based on current or historical purchase behavior the customer has exhibited. Looking at aggregate data (multiple consumers, multiple purchase points), you'll start to see trending in what products or website areas are more popular with consumers who bought X and are considering the purchase of Y. Amazon.com already does this and their metrics are a value-add for everyone looking at it. The consumer is given a feed of popular products purchased by other registered site users. The company's marketing team has a lot of supporting data statistics to provide to affiliate merchants and advertisers, and guest users can see where else on the site to look for things most similar to their search.