Absolutely. A really interesting case of this is the Chamizal Dispute in 1963 between the United States and Mexico where the Rio Grande changed its course effectively giving the United States a piece of Mexico. In this case, they actually decided to redirect the river. Here's a link to the [Texas State Historical Association's] (http://www.tshaonline.org/handbook/online/articles/nbc01) article on the dispute. It gives a nice overview. Also here's a copy of the [treaty] (http://www.ibwc.gov/Files/ChamizalConvention1963.pdf). The [US/Mexico Boundary and Water Commission] (http://www.ibwc.gov/) have some interesting links if you're interested in other issues that might arise when two countries have to share a body of water.
An AskHistorians question I can answer! I learned about this instance last semester. In 1885, Serbia declared war on Bulgaria. In reality, the Serbian government feared growing Bulgarian power after Bulgaria annexed the ethnically Bulgarian province of Eastern Rumelia. However, the Serbians claimed border integrity as their casus belli. Part of the Serbian-Bulgarian border was formed by the River Timok, which had slowly been changing its course. Finally, a large storm caused a diversion of the river which left a Serbian garrison on the now Bulgarian side of the river. After requesting the Serbs leave and being refused, the Bulgarians expelled them by force. The Serbs then declared war. Bulgaria's army was placed to defend against the Ottomans, on the other side of the country, and lead by the inexperienced king of Bulgaria, Alexander of Botenberg. What's more, the Bulgarian officer corps had been composed almost entirely of Russian officers, who had been withdrawn by the tzar after Eastern Rumelia was annexed. With all this in mind, the Serbs expected an easy victory. However, Alexander managed to move his army across the country with remarkable speed. A Bulgarian army of 10,000 men defeated a Serb force of 28,000 at the Battle of Slivinitsa. The successful Bulgarians even went on to counterattack into Serbia. At this point, Austria-Hungary intervened, demanding an end to the war. A status-quo peace agreement was then signed. While there were no physical effects on either country, Bulgaria's unification was cemented and Serbia's national prestige suffered a significant blow. And that was the Serbo-Bulgarian War. The whole thing lasted two weeks, by the way.
Source:The Palgrave Concise Historical Atlas of the Balkans.
Yes! The Rio Grande shifted between 1852-1873 with a later channel being dug in 1899. This shifted the border in a number of place leaving American territory on the south side of the river and Mexican territory on the north. The Chazimal dispute, as it is known, was not resolved until 1963. Chazimal Dispute The Legal Procedings
Interesting you would ask because I just learned about a US case like this in school. In Nebraska v. Iowa the states were trying to settle a dispute that arose when the path of the Missouri river changed. Essentially if the boundary was to still be determined by where the river currently flowed it meant that Iowa was gaining land that was formerly part of Nebraska.
To determine where the new boundary lay they looked at two principles from common law; the Rule of Accretion and the Rule of Avulsion. When a river abandons its old bed suddenly and seeks a new bed the change is called avulsion and the boundary is still drawn where the river used to flow. When a river changes course through a gradual change in its banks it is called accretion and the boundary is drawn between the middle of the two banks wherever they may now be.
In this case the court found that the change in the Missouri river that created the land in dispute was done by process of avulsion and thus the boundary remained where it had existed before the river shifted. This is one of the "textbook" cases in US law for boundary disputes between states that have a river boundary. I did a little research and it seems like the principles of avulsion and accretion have also been long recognized internationally. In fact these principles have been used since the Romans. I don't really know any details about any international cases, but the principles involved in the Nebraska v. Iowa seem nearly identical to the use of accretion and avulsion internationally.
Edit: Also here's the full opinion if you want to read it, but the case brief did a good job at describing the relevant facts and law. The second article I linked also does a good job of talking about Nebraska v Iowa, but focuses more on the evolution of the accretion/avulsion principles in an international setting. Apparently when Mexico and the US drew up the border through the Rio Grande they understood that accretion may have a potential impact on where the physical border between the countries would lie in the future.
Piggybacking on OP's question, has any state or nation purposely changed, or proposed to purposely change, the route of a river for the purpose of shifting borders without the other neighboring party's consent?
You didn't happen to just see the post about the river changing over time did you?