- Are there any other sites I should know about?
- How do you all feel about competitions where the host intends to profit from competitors' submissions?
Isabelle Guyon (working with many colleagues) has organised a series of machine learning challenges, see the website for details of previous challenges. The competitions are usually part of the programme of a conference, but attendance at the event is optional, and they are a good test of the tools in ones toolbox!
Here are some nice datasets: http://archive.ics.uci.edu/ml/
Update: The question has changed since I gave this answer.
Adding Numerai! http://www.numer.ai Numerai is an AI competition where you model the underlying fund's data - in real time - and make predictions. Download the fund's data - protected by homomorphic encryption. Upload predictions and get featured on the leaderboard. You may even get assigned profits.