I thought paper was just as bad, if not worse, because it takes more energy to produce. [Here's a random site about it, though please note that I've done pretty much nothing to vet the information.
I reuse plastic bags (garbage, traveling w/ liquids, picnics), and if I have a bunch of extras, I take them to the grocery store, where they have a recycling bin for them. I don't know if they actually get recycled (I read that they often end up in the landfill regardless), but there's a chance. I rarely get too many though because most of my shopping is at Costco, which doesn't provide them.
I disagree that a ban here is necessary or useful. I use them quite a bit, so at least for me, I'll be producing "more" waste because I'll need to buy new bags instead. Paper bags aren't as useful (can't hold liquids, are more rigid, break easily), and I always seem to forget my reusable bags.
I wish more stores would follow Costco's lead and reuse those cardboard trays, which are just as useful for carrying groceries to/from the car and are obviously recyclable and biodegradable. Honestly, I prefer them most of the time because they keep things from rolling around, I can carry more in one trip to the house, and it's easier to see where certain things are for organizing later.
What we need isn't a plastic bag ban, but maybe a tax on them based on the cost of cleaning up discarded plastic bags. It costs $0.05-0.15/bag to buy small garbage bags (bathrooms, office, etc), so the tax shouldn't be more than that. Charging for plastic bags seems to work, so why not just do that instead of a ban? Those of us who find value in these bags can continue to use them (I love them for dirty diapers, rotten food, and other stuff that shouldn't hang around the house for days), while those who don't can use other bags.