That's what we do, that or cloth supermarket bags, which can be used for years, or a wicker basket, if we go on foot to the shops or just need a few items.
At work, I have about 4 carrier bags, which I've been re-using for over a year, for when I do my lunchtime shopping - I usually buy 2-3 days worth of lunches at the supermarket up the road.
"Whilst a ban would have a positive effect on the environment, to ban plastic carrier bags in the whole of Europe would conflict with EU internal market regulation and the international trade agreements. Additionally a ban would have a negative affect on the 275 producers of bags and their 17,500 employees, possibly driving them to bankruptcy"
So? Get them weaving cloth bags instead, better for the environment, longer lasting. Just because a "dirty" industry employs people, doesn't mean that it shouldn't be cleaned up.