Serindipitor is an interesting iPhone app that gives you walking directions that are designed to encourage serendipitous experiences. The app combines directions generated by Google Maps with instructions for action and movement inspired by Fluxus, Vito Acconci, and Yoko Ono, among others.
To use the app you just need to enter a starting point and a destination. The app then maps your route with added suggestions for possible actions to take at given location. The actions are "designed to introduce small slippages and minor displacements within an otherwise optimized and efficient route".
A really cool feature of the application is that you can get directions based on the time you have available. Therefore it is possible to get walking directions not just for the quickest route but that match the time you have available.