Pros: Lots of places give them away for free, reasonably sturdy
Cons: Don't last forever if you're carrying heavy stuff a lot
These are a great utilitarian bag. Most places that give away free reusable bags give away Green Bags (of course, branded with their sweet, sweet green message). I have at least 4 floating around between work and home from the Ferry Plaza Farmers Market in San Francisco, from West Coast Green...I think I even have one from Marin County.
In any case, they fold up pretty easily (once you take out the plastic bottom) and are very light weight so it's easy to stick one in your pocket or in another bag. They don't keep their shape very well if you take out the bottom, so beware before you lose it (I've definitely misplaced mine so I end up carrying around rather oddly shaped bags from the grocery store with all sorts of lumps and bumps in the bottom of the bag).
In terms of style, they're really nothing all that special. They're square. They have straps. They hold stuff. The most distinctive feature really depends who has branded yours. But they are definitely practical. The only thing is that they don't last forever (unlike some of my heavier duty canvas bags). If you're carrying a lot of heavy stuff around (and doing it frequently), your straps may start wearing on the seams where they're connected to the bag.
But who can argue when you get something for free!