What are some easy to learn machine-learning applications? Being new to machine-learning in general, I'd like to start playing around and see what the possibilities are.

I'm curious as to what applications you might recommend that would offer the fastest time from installation to producing a meaningful result.

Also, any recommendations for good getting-started materials on the subject of machine-learning in general would be appreciated.
I would recommend to start with some MOOC on machine learning. For example Andrew Ng's course at coursera.

You should also take a look at Orange application. It has a graphical interface and probably it is easier to understand some ML techniques using it.