I'm kind of interested if you could point us in the direction of specific techniques. I always thought neural nets and genetic algorithms were interesting and I'm curious what other techniques are out there.
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.)