already out of date and is of very limited use

Depends on the type of the information, news: yes,information about biology, or Geo-Information or encyclopedic: not so fast. on other hand we now have access to real time data.

     Weather scientists have been collection data since the beginning of the century and they are still no better at predicting the weather than they were at the beginning of the century. 

Predicting Weather is near impossible in theory forget the practice. its a chaotic system, generally in data science we are trying to predict things which we know can be predicted, such as determining whether an article is relevant to a topic for example. Humans can do that very well but for machines to do it you need more data.

     They have tons of data on markets but they still can't figure out what makes markets tick. 

Again markets are chaotic and are affected by things like low probability events. You can do predict some patterns using information asymmetry, thats what all those traders at Goldman Sachs and other firms do.

    We need generative models that explain how the data is being generated and why it is being generated in a certain way.

The systems that we are interested in have complex models, and generating them from first principles isnt always as easy, additionally even if you do generate you need to test them against real world data. Rather than using the normal hypothesis - experiment cycle, it makes more sense to look for predictable patterns in data.

    I don't think the results have been that impressive.

Thats because you are out of touch with the field. Look at Google's Statistical Translation results, for example, they beat every generative model around the town. Or netflix's prize for recommendation system.

As someone interested in Data Science and been quite involved with it for few years as a student and an intern let me try to explain why data science is now becoming an important area:

1. We now have a lot of data in a machine readable format:

Unlike few years ago we now have huge datasets publicly available they, you have topic specific datasets such as Geo Names, Linked Geo data to much more wide encyclopedic datasets such as Wikipedia Data Dump, Freebase, Open Cyc, DBPedia.

We also have huge amount of user generated data, E.g. I have on my computer right now a huge chunk of twitters follower network consisting of 35 million users(I am writing an open source whom to follow system). Additionally I also have 100 million tweets.

2. Not just data we now have access to real time data:

You can access the public twitter time-line, using their streaming api, there are quite a few pubsubhubub systems out there which combine information from disparate sources and provide you unified source.

3. Moreover we have tools to handle the deluge [well sort off]:

Thanks to Google, Apache, Yahoo, Facebook we now have Hadoop , Map Reduce, Pig and other tools which make job of parallelizing processing of the data easier.

5. We have a Scalable on demand infrastructure in place:

Using AWS we can buy processing power as needed. It would have been impossible earlier, I recently bought a high memory instance with 17GB Ram for 50 cents an hour for 10 hours to run some jobs. It would have been impossible few years ago. We can now also deploy web apps very easily using Google App engine and dont need to even pay a penny, this enables us to create nice interfaces for visualization and querying for the data at a low initial cost.

Finally we are slowly building infrastructure to sell datasets or custom apps. E.g. Amazon Dev Pay or Infochimps.

The name data science can though be misleading, if you are a student that would mean taking course in Machine Learning, Data Mining, Information Retrieval, Statistics, Distributed Computing, Databases.