Somewhat relevant: My brother attended a conference where a speaker said that gait of human beings are so unique that an individual can be identified with 100% certainty using the accelerometer of the phone in their pocket.
I worked in a lab at Univserity that had several projects using gait analysis. It is very identifying, but much harder to collect than this kind of data -- you need a physical device on the target.
Still, it could be very useful for intelligence agencies. If they have identified that a phone is being used by a terrorist they can identify which terrorist is carrying it if they're able to get access to its accelerometer. Or they could gain access to millions of phones' accelerometers and identify which ones are being used by known terrorists. At the very least I expect to see it in some spy movies in the next few years.
Yes, but I don't think the phone companies save your accelerometer data like they save your phone call metadata. You'd have to get access to the phone's accelerometer somehow.
EDIT: Found a paper on the subject from 2009: http://www.cs.yale.edu/homes/mfn3/pub/mfn_gait_id.pdf
EDIT 2: Found another paper from 2012 claiming 99.4% accuracy: http://users.ece.cmu.edu/~juefeix/btas_2012_felix.pdf