I came across this brief article quite at random but it would appear to hold some possiblilities for an plastic bag alternative, considerations would obviously need to be made for sustainability, whether it can be recycled and whether it is biodegradable but it may offer an alternative:
The original article from Engadget is reproduced below, and the original can be found here:
" So much for Ballmer's vision of a paperless world -- that is, if the mighty nanofiber paper has anything to do with it. This new paper is made out of the same cellulose your regulation legal pad, but scientists at the Royal Institute of Technology in Stockholm, Sweden were able to get the fiber so small and defect-free in this version -- about 1,000 times smaller -- that it's more than seven times as strong. By breaking down wood pulp with enzymes and beating it mechanically and then treating the tiny fibers with carboxymethanol, they were able to get the new paper to a tensile strength of 214 megapascals (MPa) compared with the normal 30 MPa. So, why should you care? It's entirely possible that this stuff could replace plastic bags at stores without all the petroleum waste. "
I think its also worth mentioning one witty comment by TomTom2007:
"no more paper cut... with this thing your whole finger will be gone!"