What do you call the shop on the corner?

What do you call the shop where you get your miscellaneous stuff? I grew up in Toronto, where they were called "convenience stores," "smoke shops," and sometimes "Becker's" or "Mac's" (names of chains that got genericized). In New York, I learned to call them "bodegas." In Montreal, "depanneurs" or "the dep". In Costa Rica, we went to the pulperia (or "pulpe") for supplies, and in Honduras, we went to the "super." Here in London, they're "bottle shops," "off-licenses," "newsagents," "offies," and "cornershops" (not all identical in meaning).

What do you call 'em?
(Image: Cheap Booze, a Creative Commons Attribution-ShareAlike image from Fabbio's Flickr stream)