Deepdraw is a simple project which you can label your own handwritten digits, and train a convolutional neural network on them.
A live example of the project can be found at http://deepdraw.herokuapp.com (it can take a while to load for the first time since its a free heroku dyno :)). Select "test" on the home page, draw any digit on the white space and click on the "Send" button. Then the prediction will appear at the bottom.