I have always loved the idea of AI and evolutionary algorithms. Unfortunately, as we all know, the field hasn\'t developed nearly as fast as expected in the early days.
One of the most interesting things in AI, for me, is a very old discussion started by Rodney Brooks about his behavioral architecture called subsumption architecture.
He completely abandons all kinds of symbolic representation, and always says: take the world as your model. This saves the robot from generating a wrong world view and all complicated issues in correcting the model.
He published many interesting books and was one of the first persons in the embodied cognition approach that is used a lot in research at the moment.
Interesting reading material can be found on http://people.csail.mit.edu/brooks/index.html. Some of his later publications get very philosophical, but the earlier descriptions of the robots and how their behavior emerged from a simple set of rules and actions are worth reading.
Slightly outside of the traditional AI realm, are HTMs (Hierachical Temporal Memory) as developed at Numenta. This technology is still in its early stages but shows promises in the targeted "WOW factor" areas.
Check out http://www.wolframalpha.com/ (probably falls more under computational knowledge)
I found the recent research of evolution and cooperation among robots very intriguing. This blog entry gives a good summary of the experiment and its results. Most interesting to me was the observed behavior of both martyr AI and "evil" AI.
You might be asking an incomplete question. You are saying "what are great answers", but just like the Hitchhikers guide to the galaxy, when the best computer gives "42" as an answer, you want to know what is the question.
There are some "best questions" that drive some great answers. Some really useful answers are in things that look mundane. The "traveling salesman problem" means a lot of cost or money for FedEx. Dijkstra's algorithm drives the paths packets on the internet actually follow.
De'Morgans laws are quite cool too - they allow minimization of gates in computer chips to do the same job. They are automated and work on the billions of gates in computer chips. It likely touches as much as a third of a trillion dollars in computer-hardware based value-creation per year. I'm not talking what people do with them, I'm just talking "them".
These may seem mundane, but they are neat to me.
I also like the evolutionary antenna. I'm pretty sure that when Musk says that AI presents an existential threat, he is referring to the power of evolutionary algorithms. There is a much more modern version of that on one of the Mars rovers - and humans couldn't invent it (alone), but they can set up computers that can.
There is an ambitious open source Java library called CIlib that provides a host of Computational Intelligence methods. It is currently being used at University level by a research group to advance their own research.