What are areas where you can program artificial intelligence?

I recently started reading the book Programming Collective Intelligence. It's an excellent book which discusses exactly what you are looking for - using AI techniques in web applications.

The book is written clearly, is easy to understand, explains everything in terms of real applications (it covers how some commonly used technology works: Google Pagerank, Amazons recommendation system, matchmaking websites, link recommendation systems, bayesian spam filters and more) and it uses actually useful examples using real data (ebay API, facebook API etc are used to collect data). In one chapter, it even explains how you can draw graphs (I mean the data structure, not bar/line/etc graphs) optimally (so that no nodes are too close together, minimum overlapping lines etc), which could be useful for, for example, mapping social networks.

I would recommend having a look at it and see the different ways AI can be applied to web applications.

As a counter-example, parsing data acquired from water testing equipment would probably be a bad place to use artificial intelligence:

The Daily WTF: No, We Need a Neural Network

Just a reminder for all of us to choose the right tool for the right job.

You probably could analyze the behavior of the visitors of your web applications ; how do they navigate inside the website to provide a better, optimized interface. Now it depends on what kind of web applications you're working on. For on line shopping you can come with suggestions extrapolated from customers habits.

You can also detect "abnormal" behavior and fraud. Fraud and bot detection can take advantage of AI.