I've been meaning to mention this project for a while now: Kinetica: Naturalistic Multi-touch Data Visualization by Jeff Rzeszotarski and Niki Kittur from Carnegie Mellon's HCI team is a fascinating look at what interaction with data can be like when you start from a purely touch-based premise.
The basic idea is to have every data point as an actual point on screen and give people several physics-inspired tools to explore it. Tools shown in the video are "walls" that filter for certain criteria and free-form "magnets" that attract data points, again based on certain criteria:
This concept was so appealing that Kinetica spawned a startup: DataSquid takes the same approach and lets you analyze your data using these multi-touch physics. Here's a demo from their website:
It's still invite-only, but it looks like it could have a great future! Dare I say Multi-touch Tableau?