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...
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.)
* 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...