Call me old school, but I don't see why you can't run "minimalist" by removing the insole of an already lightweight racing flat. Back in my day the popular shoe of choice was the Onitzuka Tiger, shoe that offered no protection other than a thin rubber sole. We had to run light on our feet!
Take a look at some of the lastest 2011 racing flats at competitor.com.
If you want to really go outside the box, , I done some occasional slow jogging in an old pair of $15 Kodomo Aquarius sandals I picked up at a Big 5 store (I added a thin innersole from another pair of running shoes). Unfortunately, from what I gather Croc's filed a patent infringement claim and they may have been discontinued.
I love these sandals and wish I could get another pair.
Other options- go to invisibleshoe.com
and check out their Huarache Sandal kit or Luna Sandals designed by Barefoot Ted. ZEMgear.com is another company I am not familiar with but looks interesting.
For more minimalist options, check out amazon.com.