How much of a difference does a worn tire make?

A new BMW 3 series and a pickup truck are tested using three sets of tires.

One brand new (10/32 of tread), one with 4/32 of tread remaining, and one with 2/32 of tread remaining. Oh, and by the way if you have less than 2/32 remaining you won't pass inspection.

Test was done to see stopping distance on wet roads. The results are frankly a bit scary:
http://www.tirerack.com/videos/index.jsp?video=5

For reference here are some "penny tests" you can do to figure out what your tire depth is:
http://www.tirerack.com/tires/tiretech/techpage.jsp?techid=51

Excuse me while I shop for new tires! (well done tirerack sales team....well done...)