When I was first learning about neural networks, I came up with the idea of de-convolutional networks: http://www.matthewzeiler.com/

Also, I think this is not totally uncommon. I think this suggests that there is low-hanging fruit in crowd-sourcing ideas from non-experts.

Another related thing that happens is that I'll be reading a book, and I'll have a question/thought that gets talked about later in the book.