Fabric
I have several cloth bags from stores, and also from trade shows & such. They have been surprisingly durable. I keep a few at work, a few at home, and some in the car. We sort of have a community stash at the office that people also use from.
I was just talking to my neighbor about how freaking handy they are. I use them for everything. I used to get paper ones periodically to put recycled newspaper in, but don't need anymore. We have new bins for recycling, and everything can just get dumped in them. Also get newspaper delivered to my Kindle, so I only get the Sunday edition on paper.
If I forget bags, or need extras, I'll get plastic ones. My city accepts them with recycling. In most stores you get .05 off for bringing your own. Across the river in DC there is a .05 bag surcharge, ostensibly for river cleanup. A lot of people b*tched at first, but it seems everybody has adapted, and true you don't see bags stuck in fences and trees so much. By most measures it has been a success.
Oh, I do wash them periodically, and try to segregate their uses.