Point cloud of a scan of a stone face from the Henry Bowen Anthony fountain in Lippit Park at the head of Blackstone Boulevard in Providence RI. Available on Thingiverse.
Download Meshlab
Download Meshmixer

The Kinect is good for creating scans of large objects, like people. It is not good for capturing fine detail and may blur facial features slightly. You need a good graphics card to run ReconstructMe and a Microsoft Kinect.
123D catch photoscene of a skull.
You can use your iPhone, iPad or regular digital camera.
This video tutorial is a little out of date now (there is a more concise / updated version of how to clean up these scans in Chapter 9 of Getting Started with MakerBot, but it is Tony Buser's seminal tutorial of how to clean up Reconstruct Me scans. It uses all of the mesh editing software above. It also feaures AS220 Labs member Matt Stultz.
3D Scan Cleanup from Tony Buser on Vimeo.