Plastic bags are the best thing both for the enviornment and for cost.
Paper is the absolute worst thing for landfills: studies have shown that after 20 years paper is still clogging landfills! And paper that is burned adds huge amounts of CO2 into the atmosphere.
Reusable cloth bags sound like a great idea but unless you are a granny carrying one bag home, they are stupid: I carry 25-30 bags home from the grocery, should I buy 20 cloth bags, cloth bags made of oil-dependent, fert-rich cotton, bleached with acids, dyed with chem dyes? Or should I buy 20 bags made from oil-based synthetic fabrics, putting me in a worse place than using the cheap plastic bags? Bags that are eventually wear and wind up in landfils anyway?
Plastic bags are light, cheap, and biodegradable. And in a well engineered landfill plastic bags actually generate useable energy by decomposing quickly into recoverable methane. Some landfills (eg, Rochester, Mn) actually are able to put useable power back into the electrical grid from the methane they reclaim. The plastic is also recycleable, where plastic recycling is available.
It is enviornmentally irresponsible to use anything but the plastic bags.
More info: http://www.pouch-bag.com