As an AI researcher, I get suspicious when I see anyone talking about Genetic Algorithms and Neural Nets. These are techniques that current researchers simply do not use (Neural Nets are used very sparingly, GAs should never be used at all). They make up for their technical failings by being approachable, particularly for journalists. In short, these methods intuitively sound like they should work much better than they actually do.
Neural nets and genetic algorithms are plenty interesting, it's just that they're way more interesting than they are useful. (Also note I didn't say useless. Just, not that useful.)
For Machine Learning type applications, SVMs are very popular. Briefly, both sufficiently deep neural nets and sufficiently dimensional SVMs are arbitrarily expressive, but SVMs give you a better perspective on what is actually happening with your problem. If you're interested in Machine Learning, you should check out Andrew Moore's very well-written tutorials: http://www.autonlab.org/tutorials/list.html
Layers of unsupervised learners (clustering) feeding into a supervised learner form a very powerful technique known as deep learning. This technique hasn't found a niche though and can be outperformed by shallower methods for much of where they are used [1]. And due to all this big data mumbo jumbo on-line learning methods are getting to be more important.
[1] http://ai.stanford.edu/~ang/papers/nipsdlufl10-AnalysisSingl...
* Actually its not quite any since it holds not exactly but to a very very good approximation and there are a few, like Coevolutionary approaches which provide a loophole out of that. So that might be something you want to look at.
- http://www.no-free-lunch.org/ - http://cs.calstatela.edu/wiki/images/1/15/Wolpert-Coevolutio...
Then there are auto-encoders, Restricted Boltzmann machines and Deep Belief Nets that are certainly getting a lot of attention and are a type of neural network.
For those unlearned in AI, an analogy: the original article reads like someone talking about how they used Haskell monads to add 2 + 2.