When a river changes course on its flood plain, it can leave an entire bend of the river cut off from the new flow, forming an oxbow lake. Seen in bright blue in this shot of the Songhua River in northeast China, they are usually narrow crescents.
Here's a great timelapse over 32 years of the same stretch of river:
These bends, technically called meanders, can also bee seen on this historic map of the Mississippi River between Missouri and Louisiana
Historically, people who own land on these flood plains sometimes try to cut off a meander by hand, as described by Mark Twain:
The water cuts the alluvial banks of the 'lower' river into deep horseshoe curves; so deep, indeed, that in some places if you were to get ashore at one extremity of the horseshoe and walk across the neck, half or three quarters of a mile, you could sit down and rest a couple of hours while your steamer was coming around the long elbow, at a speed of ten miles an hour, to take you aboard again. When the river is rising fast, some scoundrel whose plantation is back in the country, and therefore of inferior value, has only to watch his chance, cut a little gutter across the narrow neck of land some dark night, and turn the water into it, and in a wonderfully short time a miracle has happened: to wit, the whole Mississippi has taken possession of that little ditch, and placed the countryman's plantation on its bank (quadrupling its value), and that other party's formerly valuable plantation finds itself away out yonder on a big island; the old watercourse around it will soon shoal up, boats cannot approach within ten miles of it, and down goes its value to a fourth of its former worth. Watches are kept on those narrow necks, at needful times, and if a man happens to be caught cutting a ditch across them, the chances are all against his ever having another opportunity to cut a ditch.
(thanks RickMycroft & phidauex)